angle - the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

4 divided by sin60 degrees

4 divided by sin60 degrees.
We can write as 4/sin(60).
[URL='https://www.mathcelebrity.com/anglebasic.php?entry=60&coff=&pl=sin']Using our trigonometry calculator[/URL], we see sin(60) = sqrt(3)/2.
So we have 4/sqrt(3)/2.
Multiplying by the reciprocal we have:
4*2/sqrt(3)
[B]8/sqrt(3)[/B]

A 12 feet ladder leans against the side of a house. The bottom of the ladder is 9 feet from the side

A 12 feet ladder leans against the side of a house. The bottom of the ladder is 9 feet from the side of the house. How high is the top of the ladder from the ground? If necessary, round your answer to the nearest tenth.
We have a right triangle, where 12 is the hypotenuse. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=9&hypinput=12&pl=Solve+Missing+Side']Using our right triangle calculator[/URL], we get:
side = [B]7.9[/B]

A 13 ft. ladder is leaning against a building 12 ft. up from the ground. How far is the base of the

A 13 ft. ladder is leaning against a building 12 ft. up from the ground. How far is the base of the ladder from the building?
This is a classic 5-12-13 pythagorean triple, where the hypotenuse is 13, and the 2 sides are 5 and 12. The building and the ground form a right triangle.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=12&hypinput=13&pl=Solve+Missing+Side']You can see the proof here[/URL]...

A 13ft ladder leans against the side of a house. The bottom of the ladder is 10ft from the side of t

A 13ft ladder leans against the side of a house. The bottom of the ladder is 10ft from the side of the house. How high is the top of the ladder from the ground? If necessary, round your answer to the nearest tenth.
We have a right triangle. Hypotenuse = 13, one leg = 10.
We use our [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=10&hypinput=13&pl=Solve+Missing+Side']Pythagorean theorem Calculator to solve for the other leg[/URL]:
s = [B]8.3066[/B]

A 5 foot ladder is leaning against a wall. If the bottom of the ladder is 3 feet from the base of th

A 5 foot ladder is leaning against a wall. If the bottom of the ladder is 3 feet from the base of the wall, how high up the wall is the top of the ladder?
The answer is [B]4[/B]. Since we have a right triangle, with special ratio 3-4-5.
The ladder represents the hypotenuse.

A 50-foot pole and a 70-foot pole are 30 feet apart. If you were to run a line between the tops of t

A 50-foot pole and a 70-foot pole are 30 feet apart. If you were to run a line between the tops of the two poles, what is the minimum length of cord you would need?
The difference between the 70 foot and 50 foot pole is:
70 - 50 = 20 foot height difference.
So we have a right triangle, with a height of 20, base of 30. We want to know the hypotenuse.
Using our [URL='https://www.mathcelebrity.com/pythag.php?side1input=20&side2input=30&hypinput=&pl=Solve+Missing+Side']Pythagorean theorem calculator to solve for hypotenuse[/URL], we get:
hypotenuse = [B]36.06 feet[/B]

A 74 inch rake is Leaning against a wall. The top of the rake hits the wall 70 inches above the grou

A 74 inch rake is Leaning against a wall. The top of the rake hits the wall 70 inches above the ground. How far is the bottom of the rake from the base of the wall?
We have a right triangle.
Hypotenuse is the rake length fo 74 inches. One of the legs is 70. We [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=70&hypinput=74&pl=Solve+Missing+Side']use our right triangle calculator to solve for the other leg[/URL]:
[B]24 inches[/B]

A bag of fertilizer covers 300 square feet of lawn. Find how many bags of fertilizer should be purch

A bag of fertilizer covers 300 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 290 feet by 150 feet.
The area of a rectangle is length * width, so we have:
A = 290 * 150
A = 43,500 sq ft.
Now, to find the number of bags needed for a 300 square feet per bag of fertilizer, we have:
Bags Needed = Total Square Feet of Lawn / Square Feet covered per bag
Bags Needed = 43,500 / 300
Bags Needed = [B]145[/B]

A beach volleyball court is 10 yards wide and 17 yards long. The rope used for the boundary line cos

A beach volleyball court is 10 yards wide and 17 yards long. The rope used for the boundary line costs $2.00 per yard. How much would it cost to buy a new boundary line for the court?
[U]Approach:[/U]
[LIST]
[*]A volleyball court is shaped as a rectangle.
[*]And the boundary line runs on the perimeter of the rectangle.
[*]So we want the perimeter of the rectangle
[/LIST]
Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=17&w=10&a=&p=&pl=Calculate+Rectangle']rectangle calculator with length = 17 and width = 10[/URL], we have:
P = [B]54[/B]

A bird was sitting 12 meters from the base of an oak tree and flew 15 meters to reach the top of the

A bird was sitting 12 meters from the base of an oak tree and flew 15 meters to reach the top of the tree. How tall is the tree?
So we have a [U]right triangle[/U]. Hypotenuse is 15. Base is 12. We want the length of the leg.
The formula for a right triangle relation of sides is a^2 + b^2 = c^2 where c is the hypotenuse and a, b are the sides
Rearranging this equation to isolate a, we get a^2 = c^2 - b^2
Taking the square root of both sides, we get a = sqrt(c^2 - b^2)
a = sqrt(15^2 - 12^2)
a = sqrt(225 - 144)
a = sqrt(81)
a = [B]9 meters[/B]

A chalkboard is 3 feet tall and 4 feet long. What is its perimeter

A chalkboard is 3 feet tall and 4 feet long. What is its perimeter
A chalkboard is a rectangle. So the perimeter is:
2l + 2w
Using [URL='https://www.mathcelebrity.com/rectangle.php?l=4&w=3&a=&p=&pl=Calculate+Rectangle']our rectangle calculator[/URL], we get:
P = [B]14[/B]

A child's bedroom is rectangular in shape with dimensions 17 feet by 15 feet. How many feet of wallp

A child's bedroom is rectangular in shape with dimensions 17 feet by 15 feet. How many feet of wallpaper border are needed to wrap around the entire room?
A rectangle has an Perimeter (P) of:
P = 2l + 2w
We're given l = 17 and w = 15. So we have:
P = 2(17) + 2(15)
P = 34 + 30
P = [B]64[/B]

A computer screen has a diagonal dimension of 19 inches and a width of 15 inches. Approximately what

A computer screen has a diagonal dimension of 19 inches and a width of 15 inches. Approximately what is the height of the screen?
We have a right triangle, with hypotenuse of 19, and width of 15.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=15&hypinput=19&pl=Solve+Missing+Side']Using our right triangle calculator, we get [/URL][B]height = 11.662[/B]

A diving board is 10 feet long and 1 foot wide. What is its area?

A diving board is 10 feet long and 1 foot wide. What is its area?
A diving board is a rectangle. And the area of a rectangle is:
A = lw
Plugging in our numbers, we get:
A = 10(1)
A = [B]10 sq feet[/B]

A family room measures 15.6 feet long and 18.4 feet wide. What is the area of the room?

A family room measures 15.6 feet long and 18.4 feet wide. What is the area of the room?
The room is rectangular. So our area A = lw.
Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=15.6&w=18.4&a=&p=&pl=Calculate+Rectangle']rectangle calculator[/URL], we get:
A = [B]287.04 square feet[/B]

A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants t

A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants the length x to be greater than 50 feet and the width y to be no more than 20 feet. Write a system to represent this situation.
Perimeter of a rectangle:
P = 2l + 2w
We have P = 165 and l = x --> x>50 and width y <= 20. Plug these into the perimeter formula
[B]165 = 2x + 2y where x > 50 and y <= 20[/B]

A flower bed is to be 3 m longer than it is wide. The flower bed will an area of 108 m2 . What will

A flower bed is to be 3 m longer than it is wide. The flower bed will an area of 108 m2 . What will its dimensions be?
A flower bed has a rectangle shape, so the area is:
A = lw
We are given l = w + 3
Plugging in our numbers given to us, we have:
108 = w(w + 3)
w^2 + 3w = 108
Subtract 108 from each side:
w^2 + 3w - 108 = 0
[URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2%2B3w-108%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get:
w = (9, -12)
Since length cannot be negative, w = 9.
And l = 9 + 3 --> l = 12
So we have [B](l, w) = (12, 9)[/B]
Checking our work, we have:
A = (12)9
A = 108 <-- Match!

A framed print measures 80cm by 65cm. The frame is 5cm wide. Find the area of the unframed print

A framed print measures 80cm by 65cm. The frame is 5cm wide. Find the area of the unframed print.
We subtract 5 cm from the length and the width to account for the frame:
Unframed Length: 80 - 5 = 75
Unframed Width: 65 - 5 = 60
Area of the unframed rectangle is:
A = lw
A = 75(60)
A = [B]4,500 sq cm[/B]

A garden has a length that is three times its width. If the width is n feet and fencing cost $8 per

A garden has a length that is three times its width. If the width is n feet and fencing cost $8 per foot, what is the cost of the fencing for the garden?
Garden is a rectangle which has Perimeter P of:
P = 2l + 2w
l = 3w
P = 2(3w) + 2w
P = 6w + 2w
P = 8w
Width w = n, so we have:
P = 8n
Cost = 8n * 8 = [B]64n dollars[/B]

A helicopter rose vertically 300 m and then flew west 400 m how far was the helicopter from it’s sta

A helicopter rose vertically 300 m and then flew west 400 m how far was the helicopter from it’s starting point?
The distance forms a right triangle. We want the distance of the hypotenuse.
Using our [URL='http://www.mathcelebrity.com/pythag.php?side1input=300&side2input=400&hypinput=&pl=Solve+Missing+Side']right triangle calculator[/URL], we get a distance of [B]500[/B].
We also could use a shortcut on this problem. If you divide 300 and 400 by 100, you get 3 and 4. Since we want the hypotenuse, you get the famous 3-4-5 triangle ratio. So the answer is 5 * 100 = 500.

A ladder 25 feet long is leaning against a wall. If the base of the ladder is 7 feet from the wall,

A ladder 25 feet long is leaning against a wall. If the base of the ladder is 7 feet from the wall, how high up the wall does the ladder reach?
We have a right triangle, where the ladder is the hypotenuse, and we want the measurement of one leg.
Set up the pythagorean theorem with these given items using our P[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=7&hypinput=25&pl=Solve+Missing+Side']ythagorean Theorem Calculator[/URL].
We get Side 1 = [B]24 feet.[/B]

A ladder is 25 ft long. The ladder needs to reach to a window that is 24 ft above the ground. How fa

A ladder is 25 ft long. The ladder needs to reach to a window that is 24 ft above the ground. How far away from the building should the bottom of the ladder be placed?
We have a right triangle, where the ladder is the hypotenuse, and the window side is one side.
Using our right triangle and the [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=24&hypinput=25&pl=Solve+Missing+Side']pythagorean theorem calculator[/URL], we get a length of [B]7 ft [/B]for the ladder bottom from the wall.

A ladder rests 2.5 m from the base of a house. If the ladder is 4 m long, how far up the side of the

A ladder rests 2.5 m from the base of a house. If the ladder is 4 m long, how far up the side of the house will the ladder reach?
We have a right triangle with the hypotenuse as 4, the one leg as 2.5 We want to solve for the other leg length. We use our [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=2.5&hypinput=4&pl=Solve+Missing+Side']right triangle solver[/URL] to get [B]3.122[/B]

A man stands at point p, 45 metres from the base of a building that is 20 metres high. Find the angl

A man stands at point p, 45 metres from the base of a building that is 20 metres high.
Find the angle of elevation of the top of the building from the man.
Draw a right triangle ABC where Side A is from the bottom of the building to the man and Side B is the bottom of the building to the top of the building. Using right triangle calculations, we want Angle A which is the angle of elevation.
[URL='http://www.mathcelebrity.com/righttriangle.php?angle_a=&a=20&angle_b=&b=45&c=&pl=Calculate+Right+Triangle']Angle of Elevation[/URL] which is [B]23.9625°[/B]

A parallelogram has a perimeter of 54 centimeters. Two of the sides are each 17 centimeters long. Wh

A parallelogram has a perimeter of 54 centimeters. Two of the sides are each 17 centimeters long. What is the length of each of the other two sides?
A parallelogram is a rectangle bent on it's side. So we have the perimeter formula P below:
P = 2l + 2w
We're given w = 17 and P = 54. So we plug this into the formula for perimeter:
2l + 2(17) = 54
2l + 34 = 54
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B34%3D54&pl=Solve']equation calculator[/URL], we get [B]l = 10[/B].

A playing card is 7 centimeters wide and 10 centimeters tall. What is its area?

A playing card is 7 centimeters wide and 10 centimeters tall. What is its area?
A playing card has a rectangle shape, so the area is l x w.
A = l x w
A = 10 cm x 7 cm
A =[B] 70 cm^2[/B]

A pool is 5 meters wide and 21 meter long what is the area of the pool?

A pool is 5 meters wide and 21 meter long what is the area of the pool?
A pool is a rectangle. So the area for a rectangle is:
A = lw [I]where l is the length and w is the width.[/I]
[URL='https://www.mathcelebrity.com/rectangle.php?l=21&w=5&a=&p=&pl=Calculate+Rectangle']Plugging in our width of 5 and length of 21 to our rectangle calculator[/URL], we get:
A = [B]105 m^2[/B]

A postcard is 4 inches tall and 5 inches wide. What is its area?

A postcard is 4 inches tall and 5 inches wide. What is its area?
A postcard is a rectangle. The area is 4 x 5 = [B]20 square inches[/B]

a rectangle has a length of x-7 and a width of x + 5. Write an expression that represents the area o

a rectangle has a length of x-7 and a width of x + 5. Write an expression that represents the area of the rectangle in terms of x.
Area of a rectangle (A) with length(l) and width (w) is expressed as follows:
A = lw
Plugging in our values given above, we have:
[B]A = (x - 7)(x + 5)[/B]

A rectangle has a length that is 8.5 times its width. IF the width is n, what is the perimeter of th

A rectangle has a length that is 8.5 times its width. IF the width is n, what is the perimeter of the rectangle.
w = n
l = 8.5n
P = 2(8.5n) + 2n
P = 17n + 2n
P = [B]19n[/B]

A RECTANGLE HAS A PERIMETER OF 196 CENTIMETERS. IF THE LENGTH IS 6 TIMES ITS WIDTH FIND TH DIMENSION

A RECTANGLE HAS A PERIMETER OF 196 CENTIMETERS. IF THE LENGTH IS 6 TIMES ITS WIDTH FIND TH DIMENSIONS OF THE RECTANGLE?
Whoa... stop screaming with those capital letters! But I digress...
The perimeter of a rectangle is:
P = 2l + 2w
We're given two equations:
[LIST=1]
[*]P = 196
[*]l = 6w
[/LIST]
Plug these into the perimeter formula:
2(6w) + 2w = 196
12w + 2w = 196
[URL='https://www.mathcelebrity.com/1unk.php?num=12w%2B2w%3D196&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]w = 14[/B]
Now we put w = 14 into equation (2) above:
l = 6(14)
[B]l = 84
[/B]
So our length (l), width (w) of the rectangle is (l, w) = [B](84, 14)
[/B]
Let's check our work by plugging this into the perimeter formula:
2(84) + 2(14) ? 196
168 + 28 ? 196
196 = 196 <-- checks out

a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions?

a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions?
We know the rectangle has the following formulas:
Area = lw
Perimeter = 2l + 2w
Given an area of 238 and a perimeter of 62, we have:
[LIST=1]
[*]lw = 238
[*]2(l + w) = 62
[/LIST]
Divide each side of (1) by w:
l = 238/w
Substitute this into (2):
2(238/w + w) = 62
Divide each side by 2:
238/w + w = 31
Multiply each side by w:
238w/w + w^2 = 31w
Simplify:
238 + w^2 = 31w
Subtract 31w from each side:
w^2 - 31w + 238 = 0
We have a quadratic. So we run this through our [URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2-31w%2B238%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation calculator[/URL] and we get:
w = (14, 17)
We take the lower amount as our width and the higher amount as our length:
[B]w = 14
l = 17
[/B]
Check our work for Area:
14(17) = 238 <-- Check
Check our work for Perimeter:
2(17 + 14) ? 62
2(31) ? 62
62 = 62 <-- Check

A rectangle shaped parking lot is to have a perimeter of 506 yards. If the width must be 100 yards b

A rectangle shaped parking lot is to have a perimeter of 506 yards. If the width must be 100 yards because of a building code, what will the length need to be?
Perimeter of a rectangle (P) with length (l) and width (w) is:
2l + 2w = P
We're given P = 506 and w = 100. We plug this in to the perimeter formula and get:
2l + 2(100) = 506
To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B2%28100%29%3D506&pl=Solve']type it in our search engine[/URL] and we get:
l = [B]153[/B]

A rectangular field is to be enclosed with 1120 feet of fencing. If the length of the field is 40 fe

A rectangular field is to be enclosed with 1120 feet of fencing. If the length of the field is 40 feet longer than the width, then how wide is the field?
We're given:
[LIST=1]
[*]l = w + 40
[/LIST]
And we know the perimeter of a rectangle is:
P = 2l + 2w
Substitute (1) into this formula as well as the given perimeter of 1120:
2(w + 40) + 2w = 1120
Multiply through and simplify:
2w + 80 + 2w = 1120
Group like terms:
4w + 80 = 1120
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B80%3D1120&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 260[/B]

A rectangular field is twice as long as it is wide. If the perimeter is 360 what are the dimensions?

A rectangular field is twice as long as it is wide. If the perimeter is 360 what are the dimensions?
We are given or know the following about the rectangle
[LIST]
[*]l = 2w
[*]P = 2l + 2w
[*]Since P = 360, we have 2l + 2w = 360
[/LIST]
Since l = 2w, we have 2l + (l) = 360
3l = 360
Divide by 3, we get [B]l = 120[/B]
Which means w = 120/2
[B]w = 60[/B]

A rectangular football pitch has its length equal to twice its width and a perimeter of 360m. Find i

A rectangular football pitch has its length equal to twice its width and a perimeter of 360m. Find its length and width.
The area of a rectangle (A) is:
A = lw --> where l is the length and w is the width
We're given l = 2w, so we substitute this into the Area equation:
A = (2w)w
A = 2w^2
We're given the area of the pitch is 360, so we set:
2w^2 = 360
We [URL='https://www.mathcelebrity.com/1unk.php?num=2w%5E2%3D360&pl=Solve']type this equation into our search engine[/URL], follow the links, and get:
w = [B]6*sqrt(5)
[/B]
Now we take this, and substitute it into this equation:
6*sqrt(5)l = 360
Dividing each side by 6*sqrt(5), we get:
l = [B]60/sqrt(5)[/B]

A rectangular garden is 5 ft longer than it is wide. Its area is 546 ft2. What are its dimensions?

A rectangular garden is 5 ft longer than it is wide. Its area is 546 ft2. What are its dimensions?
[LIST=1]
[*]Area of a rectangle is lw. lw = 546ft^2
[*]We know that l = w + 5.
[/LIST]
Substitute (2) into (1)
(w + 5)w = 546
w^2 + 5w = 546
Subtract 546 from each side
w^2 + 5w - 546 = 0
Using the positive root in our [URL='http://www.mathcelebrity.com/quadratic.php?num=w%5E2%2B5w-546%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get [B]w = 21[/B].
This means l = 21 + 5.
[B]l = 26[/B]

A rectangular hotel room is 4 yards by 5 yards. The owner of the hotel wants to recarpet the room wi

A rectangular hotel room is 4 yards by 5 yards. The owner of the hotel wants to recarpet the room with carpet that costs $76.00 per square yard. How much will it cost to recarpet the room? $
The area of a rectangle is length * width, so we have:
A = 5 yards * 4 yards
A = 20 square yards
Total cost = Cost per square yard * total square yards
Total Cost = $76 * 20
Total Cost = [B]$1520[/B]

A rectangular house is 68 yards wide and 112 yards long. What is its perimeter?

A rectangular house is 68 yards wide and 112 yards long. What is its perimeter?
The perimeter of a rectangle is:
P = 2l + 2w
Plugging in our length of 112 and our width of 68, we get:
P = 2(112) + 2(68)
P = 224 + 136
P = [B]360[/B]

A rectangular parking lot has a perimeter of 152 yards. If the length of the parking lot is 12 yards

A rectangular parking lot has a perimeter of 152 yards. If the length of the parking lot is 12 yards greater than the width. What is the width of the parking lot?
The perimeter of a rectangle is: 2l + 2w = P.
We're given 2 equations:
[LIST=1]
[*]2l + 2w = 152
[*]l = w + 12
[/LIST]
Substitute equation (2) into equation (1) for l:
2(w + 12) + 2w = 152
2w + 24 + 2w = 152
Combine like terms:
4w + 24 = 152
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B24%3D152&pl=Solve']type this equation into our search engine[/URL] and we get:
w =[B] 32[/B]

A rectangular piece of paper has the dimensions of 10 inches by 7 inches.What is the perimeter of th

A rectangular piece of paper has the dimensions of 10 inches by 7 inches.What is the perimeter of the piece of paper
Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=10&w=7&a=&p=&pl=Calculate+Rectangle']rectangle calculator[/URL], we get perimeter P:
P = [B]34[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters
Given l = length and w = width, The perimeter of a rectangle is 2l + 2w, we have:
[LIST=1]
[*]l = 3w
[*]2l + 2w = 56
[/LIST]
Substitute equation (1) into equation (2) for l:
2(3w) + 2w = 56
6w + 2w = 56
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']type it in our math engine[/URL] and we get:
w = [B]7
[/B]
To solve for l, we substitute w = 7 into equation (1):
l = 3(7)
l = [B]21[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters.

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters.
We're given the following:
[LIST]
[*]l = 3w
[/LIST]
We know the Perimeter (P) of a rectangle is:
P = 2l + 2w
Substituting l = 3w and P = 56 into this equation, we get:
2(3w) + 2w = 56
Multiplying through, we get:
6w + 2w = 56
(6 +2)w = 56
8w = 56
[URL='https://www.mathcelebrity.com/1unk.php?num=8w%3D56&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 7[/B]
Substitute w = 7 into l = 3w, we get:
l = 3(7)
[B]l = 21[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimens

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimensions of the room.
We're given two items:
[LIST]
[*]l = 3w
[*]P = 56
[/LIST]
We know the perimeter of a rectangle is:
2l + 2w = P
We plug in the given values l = 3w and P = 56 to get:
2(3w) + 2w = 56
6w + 2w = 56
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']plug this equation into our search engine[/URL] and we get:
w = [B]7
[/B]
To solve for l, we plug in w = 7 that we just found into the given equation l = 3w:
l = 3(7)
l = [B]21
[/B]
So our dimensions length (l) and width (w) are:
(l, w) = [B](21, 7)[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimens

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimension of the room.
We're given:
l = 3w
The Perimeter (P) of a rectangle is:
P = 2l + 2w
With P = 56, we have:
[LIST=1]
[*]l = 3w
[*]2l + 2w = 56
[/LIST]
Substitute equation (1) into equation (2) for l:
2(3w) + 2w = 56
6w + 2w = 56
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']type it in our search engine[/URL] and we get:
w = [B]7
[/B]
Now we plug w = 7 into equation (1) above to solve for l:
l = 3(7)
l = [B]21[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 64 meters. Find the dimens

A rectangular room is 3 times as long as it is wide, and its perimeter is 64 meters. Find the dimension of the room.
We're given:
[LIST]
[*]l = 3w
[*]P = 64
[/LIST]
We also know the perimeter of a rectangle is:
2l + 2w = P
We plugin l = 3w and P = 64 into the perimeter equation:
2(3w) + 2w = 64
Multiply through to remove the parentheses:
6w + 2w = 64
To solve this equation for w, we type it in our search engine and we get:
[B]w = 8[/B]
To solve for l, we plug w = 8 into the l = 3w equation above:
l = 3(8)
[B]l = 24[/B]

A rectangular room is 4 times as long as it is wide, and its perimeter is 80 meters. Find the dimens

A rectangular room is 4 times as long as it is wide, and its perimeter is 80 meters. Find the dimension of the room
The perimeter of a rectangle is P = 2l + 2w. We're given two equations:
[LIST=1]
[*]l = 4w
[*]2l + 2w = 80. <-- Since perimeter is 80
[/LIST]
Plug equation (1) into equation (2) for l:
2(4w) + 2w = 80
8w + 2w = 80
[URL='https://www.mathcelebrity.com/1unk.php?num=8w%2B2w%3D80&pl=Solve']Plugging this equation into our search engine[/URL], we get:
w = [B]10[/B]
To get l, we plug w = 10 into equation (1):
l = 4(10)
l = [B]40[/B]

A right triangle has legs of 9 feet and 12 feet. How long is the hypotenuse?

A right triangle has legs of 9 feet and 12 feet. How long is the hypotenuse?
A common right triangle ratio is 3:4:5
9 = 3 * 3
12 = 3 * 4
3 * 5 = 15, so we have [B]15 feet[/B]

A standard volleyball court has an area of 1800ft. The length is 60. What is the width of the volley

A standard volleyball court has an area of 1800ft. The length is 60. What is the width of the volleyball court
Plugging [URL='https://www.mathcelebrity.com/rectangle.php?l=60&w=&a=1800&p=&pl=Calculate+Rectangle']this into our rectangle calculator[/URL] and we get:
w = [B]30[/B]

A straight road to the top of a hill is 2500 feet long and makes an angle of 12 degrees with the hor

A straight road to the top of a hill is 2500 feet long and makes an angle of 12 degrees with the horizontal. Find the height of the hill.
Height = Distance * Sin(Horizon Angle)
Height = 2500 * [URL='http://www.mathcelebrity.com/anglebasic.php?entry=12&coff=&pl=sin']Sin(12)[/URL]
Height = 2500 * 0.207911691
Height = [B]519.78 feet[/B]

A train ticket is 8 centimeters tall and 10 centimeters long. What is its area?

A train ticket is 8 centimeters tall and 10 centimeters long. What is its area?
The ticket is a rectangle. The area is:
A = lw
Plugging in our numbers, we get:
A = (8)(10)
A = 80

A triangle has an area of 60 square inches and a base of 10 inches. What is its height?

A triangle has an area of 60 square inches and a base of 10 inches. What is its height?
A = bh/2
b = 2A/h
b = 2(60)/10
b = 120/10
b = [B]12 inches[/B]

a triangle has side lengths of 12,16, and 20 centimeters. is it a right triangle?

a triangle has side lengths of 12,16, and 20 centimeters. is it a right triangle?
First, we see if we can simplify. So we [URL='https://www.mathcelebrity.com/gcflcm.php?num1=12&num2=16&num3=20&pl=GCF']type GCF(12,16,20) [/URL]and we get 4.
We divide the 3 side lengths by 4:
12/4 = 3
16/4 = 4
20/4 = 5
And lo and behold, we get a Pythagorean Triple of 3, 4, 5. So [B]yes, this is a right triangle[/B].

A triangular garden has base of 6 meters amd height of 8 meters. Find its area

A triangular garden has base of 6 meters amd height of 8 meters. Find its area
Area (A) of a triangle is:
A = bh/2
Plugging in our numbers, we get:
A = 6*8/2
A = [B]24 square meters[/B]

A yard is 33.21 meters long and 17.6 meters wide. What length of fence must be purchased to enclose

A yard is 33.21 meters long and 17.6 meters wide. What length of fence must be purchased to enclose the entire yard?
The yard is a rectangle. The perimeter of a rectangle is:
P = 2l + 2w where l is the length and w is the width.
Evaluating, using our [URL='https://www.mathcelebrity.com/rectangle.php?l=33.21&w=17.6&a=&p=&pl=Calculate+Rectangle']rectangle calculator[/URL], we get P = [B]101.62[/B]

A young dad, who was a star football player in college, set up a miniature football field for his fi

A young dad, who was a star football player in college, set up a miniature football field for his five-year-old young daughter, who was already displaying an unusual talent for place-kicking. At each end of the mini-field, he set up goal posts so she could practice kicking extra points and field goals. He was very careful to ensure the goalposts were each straight up and down and that the crossbars were level. On each set, the crossbar was six feet long, and a string from the top of each goalpost to the midpoint between them on the ground measured five feet. How tall were the goalposts? How do you know this to be true?
The center of each crossbar is 3 feet from each goalpost. We get this by taking half of 6, since midpoint means halfway.
Imagine a third post midway between the two goal posts. It has the same height as the two goalposts.
From the center post, the string from the top of a goalpost to the base of the center post, and half the crossbar form and right triangle with hypotenuse 5 feet and one leg 3 feet.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=3&hypinput=5&pl=Solve+Missing+Side']Using the Pythagorean Theorem[/URL], the other leg -- the height of each post -- is 4 feet.

All squares are rectangles and all rectangles are parallelograms, therefore all squares are parallel

All squares are rectangles and all rectangles are parallelograms, therefore all squares are parallelograms. Is this true?
[B]Yes.[/B]
This is similar to A implies B and B implies C so A implies C also known as transitive property

Allan built an additional room onto his house. The length of the room is 3 times the width. The peri

Allan built an additional room onto his house. The length of the room is 3 times the width. The perimeter of the room is 60 feet. What is the length of the room
A room is a rectangle. We know the perimeter of a rectangle is:
P = 2l + 2w
We're given two equations:
[LIST=1]
[*]l = 3w
[*]P = 60
[/LIST]
Plug (1) and (2) into our rectangle perimeter formula:
2(3w) + w = 60
6w + w = 60
[URL='https://www.mathcelebrity.com/1unk.php?num=6w%2Bw%3D60&pl=Solve']Type this equation into our search engine[/URL] to solve for w:
w = 8.5714
Now plug w = 8.5714 into equation 1 to solve for l:
l = 3(8.5714)
l = [B]25.7142[/B]

An angle is 30 degrees less than 5 times it's complement. Find the angle.

An angle is 30 degrees less than 5 times it's complement. Find the angle.
Let the angle be a. The complement of a is 90 - a. We're given the following equation:
a = 5(90 - a) - 30 <-- Less means we subtract
Multiplying though, we get:
a = 450 - 5a - 30
a = 420 - 5a
[URL='https://www.mathcelebrity.com/1unk.php?num=a%3D420-5a&pl=Solve']Typing this equation into our search engine[/URL], we get:
a =[B] 70[/B]

An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second

An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second?
We want to convert revolutions per minute to revolutions per second:
3000 revolutions per minute / 60 seconds per minute = 50 revolutions per second
Using our [URL='http://www.mathcelebrity.com/anglecon.php?quant=50&type=revolution&pl=Calculate']revolutions to degrees calculator[/URL], we get [B]18,000[/B]

An equilateral triangle has three sides of equal length. What is the equation for the perimeter of a

An equilateral triangle has three sides of equal length. What is the equation for the perimeter of an equilateral triangle if P = perimeter and S = length of a side?
P = s + s + s
[B]P = 3s[/B]

An isosceles triangles non-congruent angle is 16 more than twice the congruent ones. What is the mea

An isosceles triangles non-congruent angle is 16 more than twice the congruent ones. What is the measure of all 3 angles?
Let the congruent angles measurement be c. And the non-congruent angle measurement be n. We're given:
[LIST=1]
[*]n = 2c + 16 <-- Twice means we multiply by 2, and more than means we add 16
[*]2c + n = 180 <-- Since the sum of angles in an isosceles triangle is 180
[/LIST]
Substitute (1) into (2):
2c + (2c + 16) = 180
Group like terms:
4c + 16 = 180
[URL='https://www.mathcelebrity.com/1unk.php?num=4c%2B16%3D180&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]c = 41[/B]
Substituting this value into Equation 1, we get
n = 2(41) + 16
n = 82 + 16
[B]n = 98[/B]

Angle of Elevation

Solves angle of elevation word problems

Angle Ratio for a Triangle

Given an angle ratio for a triangle of a:b:c, this determines the angle measurements of the triangle.

Anne wants to make a platform that is 7 feet wide and 10 feet long. If she uses boards that measure

Anne wants to make a platform that is 7 feet wide and 10 feet long. If she uses boards that measure 6 inches wide by 2 feet long, how many boards will she need to complete the job?
Area of platform which is a rectangle:
A = lw
A = 10 * 7
A = 70
Area of boards which are rectangles:
A = lw
A = 2 * 6
A = 12
We divide our platform area by our board area to get the number of boards needed:
Boards needed = Platform Area / Board Area
Boards needed = 70/12
Boards needed = 5.83333
We round up if we want full boards to be [B]6[/B]

area of a rectangle

area of a rectangle
Let l be the length and w be the width of a rectangle. The Area (A) is:
A = [B]lw[/B]

Cevian Triangle Relations

Given a triangle with a cevian, this will solve for the cevian or segments or sides based on inputs

Chris walks 12 blocks north and then 16 blocks East. How far is his home from the park

Chris walks 12 blocks north and then 16 blocks East. How far is his home from the park
We've got a right triangle. If we divide 12 and 16 by 4, we get:
12/4 = 3
16/4 = 4
Since the hypotenuse is the distance from the home to the park, we have a classic 3-4-5 right triangle.
So our hypotenuse is 5*4 = [B]20[/B]

Clock Angle

Calculate the angle on a clock between the hour and minute hands or how many times on the clock form an angle of (x°) between the minute and hour hand (backwards and forwards). Clock Angle Calculator

Complementary and Supplementary Angles

This calculator determines the complementary and supplementary angle of a given angle that you enter OR it checks to see if two angles that you enter are complementary or supplementary.

Consecutive Interior Angles

Shows you a proof of consecutive interior angles using parallel lines and a transversal

Equilateral Triangle

Given a side (a), this calculates the following items of the equilateral triangle:

* Perimeter (P)

* Semi-Perimeter (s)

* Area (A)

* altitudes (h_{a},h_{b},h_{c})

* medians (m_{a},m_{b},m_{c})

* angle bisectors (t_{a},t_{b},t_{c})

* Circumscribed Circle Radius (R)

* Inscribed Circle Radius (r)

* Perimeter (P)

* Semi-Perimeter (s)

* Area (A)

* altitudes (h

* medians (m

* angle bisectors (t

* Circumscribed Circle Radius (R)

* Inscribed Circle Radius (r)

Find an angle (theta) with 0<(theta)<360° or 0<(theta)<(2*pi) that has the same sine value as 80°

Find an angle (theta) with 0<(theta)<360° or 0<(theta)<(2*pi) that has the same sine value as 80°.
The sine is positive in Quadrant I and Quadrant II. So we find the reference angle for 80°.
It's 180 - 80 = [B]100°[/B].
This is our answer. Sin(80°) = Sin(100°)

Find x

Find x
[IMG]https://mathcelebrity.com/community/data/attachments/0/cong-angles.jpg[/IMG]
Since both angles are congruent, we set them equal to each other:
6x - 20 = 4x
To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=6x-20%3D4x&pl=Solve']type this equation into our math engine[/URL] and we get:
x = [B]10[/B]

Finding the dimensions

How do I find dimensions of a rectangle when it has been expanded?

Geometric Mean of a Triangle

Given certain segments of a special right triangle, this will calculate other segments using the geometric mean

Given the rectangular prism below, if AB = 6 in., AD = 8 in. and BF = 24, find the length of FD.

Given the rectangular prism below, if AB = 6 in., AD = 8 in. and BF = 24, find the length of FD.
[IMG]http://www.mathcelebrity.com/images/math_problem_library_129.png[/IMG]
If AB = 6 and AD = 8, by the Pythagorean theorem, we have BD = 10 from our [URL='http://www.mathcelebrity.com/pythag.php?side1input=6&side2input=8&hypinput=&pl=Solve+Missing+Side']Pythagorean Theorem[/URL] Calculator
Using that, we have another right triangle which we can use the [URL='http://www.mathcelebrity.com/pythag.php?side1input=10&side2input=24&hypinput=&pl=Solve+Missing+Side']pythagorean theorem[/URL] calculator to get [B]FD = 26[/B]

Given:

Given:

Given: WS bisects

[B]I need 36 m of fencing for my rectangular garden. I plan to build a 2m tall fence around the garden. The width of the garden is 6 m shorter than twice the length of the garden. How many square meters of space do I have in this garden?
List the answer being sought (words) ______Need_________________________
What is this answer related to the rectangle?_Have_________________________
List one piece of extraneous information____Need_________________________
List two formulas that will be needed_______Have_________________________
Write the equation for width_____________Have_________________________
Write the equation needed to solve this problem____Need____________________[/B]

Help on problem

[B]List the answer being sought (words) ______Area of the garden
What is this answer related to the rectangle?_Have_________________________
List one piece of extraneous information____2m tall fence
List two formulas that will be needed_______P = 36. P = 2l + 2w
Write the equation for width_____________w = 2l - 6
Write the equation needed to solve this problem A = lw, P = 2l + 2w[/B]

How many degrees is an acute angle

How many degrees is an acute angle
An acute angle is an angle between 0 and less than 90 degrees:
[B]0 <= a < 90[/B]

If 800 feet of fencing is available, find the maximum area that can be enclosed.

If 800 feet of fencing is available, find the maximum area that can be enclosed.
Perimeter of a rectangle is:
2l + 2w = P
However, we're given one side (length) is bordered by the river and the fence length is 800, so we have:
So we have l + 2w = 800
Rearranging in terms of l, we have:
l = 800 - 2w
The Area of a rectangle is:
A = lw
Plug in the value for l in the perimeter into this:
A = (800 - 2w)w
A = 800w - 2w^2
Take the [URL='https://www.mathcelebrity.com/dfii.php?term1=800w+-+2w%5E2&fpt=0&ptarget1=0&ptarget2=0&itarget=0%2C1&starget=0%2C1&nsimp=8&pl=1st+Derivative']first derivative[/URL]:
A' = 800 - 4w
Now set this equal to 0 for maximum points:
4w = 800
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%3D800&pl=Solve']Typing this equation into the search engine[/URL], we get:
w = 200
Now plug this into our perimeter equation:
l = 800 - 2(200)
l = 800 - 400
l = 400
The maximum area to be enclosed is;
A = lw
A = 400(200)
A = [B]80,000 square feet[/B]

If all A's are B's, then all B's are A's. Is this true?

If all A's are B's, then all B's are A's. Is this true?
[B]No.[/B]
Example:
All dogs are mammals, but not all mammals are dogs.
All squares are rectangles, but not all rectangles are squares.

If the perimeter of a rectangular field is 120 feet and the length of one side is 25 feet, how wide

If the perimeter of a rectangular field is 120 feet and the length of one side is 25 feet, how wide must the field be?
The perimeter of a rectangle P, is denoted as:
P = 2l + 2w
We're given l = 25, and P = 120, so we have
2(25) + 2w = 120
Simplify:
2w + 50 = 120
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B50%3D120&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 35[/B]

If the perimeter of a rectangular sign is 44cm and the width is 2cm shorter than half the length, th

If the perimeter of a rectangular sign is 44cm and the width is 2cm shorter than half the length, then what are the length and width?
The perimeter (P) of a rectangle is:
2l + 2w = P
We're given P = 44, so we substitute this into the rectangle perimeter equation:
2l + 2w = 44
We're also given w = 0.5l - 2. Substitute the into the Perimeter equation:
2l + 2(0.5l - 2) = 44
Multiply through and simplify:
2l + l - 4 = 44
Combine like terms:
3l - 4 = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=3l-4%3D44&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]l = 16[/B]
Substitute this back into the equation w = 0.5l - 2
w = 0.5(16) - 2
w = 8 - 2
[B]w = 6[/B]

if two angles are supplementary and congruent then they are right angles

if two angles are supplementary and congruent then they are right angles
Let the first angle be x. Let the second angle be y.
Supplementary angles means their sum is 180:
x + y = 180
We're given both angles are congruent, meaning equal. So we set x = y:
y + y = 180
To solve for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=y%2By%3D180&pl=Solve']type this equation into our search engine[/URL] and we get:
y = [B]90. <-- 90 degrees is a right angle, so this is TRUE[/B]

Isosceles Triangle

Given a long side (a) and a short side (b), this determines the following items of the isosceles triangle:

* Area (A)

* Semi-Perimeter (s)

* Altitude a (ha)

* Altitude b (hb)

* Altitude c (hc)

* Area (A)

* Semi-Perimeter (s)

* Altitude a (ha)

* Altitude b (hb)

* Altitude c (hc)

Janice says that the sum of the measures of the interior angles of an octagon is 900°. Is Janice cor

Janice says that the sum of the measures of the interior angles of an octagon is 900°. Is Janice correct? Why or why not?
She's [B]incorrect.
[/B]
The interior angle sum for a polygon is found with this formula:
Interior Angle Sum = (sides - 2) x 180°
Since an octagon has 8 sides, we have:
Interior Angle Sum = (8 - 2) x 180°
Interior Angle Sum = 6 x 180°
Interior Angle sum = 1080°

Juan runs out of gas in a city. He walks 30yards west and then 16 yards south looking for a gas stat

Juan runs out of gas in a city. He walks 30yards west and then 16 yards south looking for a gas station. How far is he from his starting point?
Juan is located on a right triangle. We calculate the hypotenuse:
30^2 + 16^2 = Hypotenuse^2
900 + 256 = Hypotenuse^2
Hypotenuse^2 = 1156
Take the square root of each side:
[B]Hypotenuse = 34 yards[/B]

Kites

This calculates perimeter and/or area of a kite given certain inputs such as short and long side, short and long diagonal, or angle between short and long side

Line Equation-Slope-Distance-Midpoint-Y intercept

Enter 2 points, and this calculates the following:

* Slope of the line (rise over run) and the line equation y = mx + b that joins the 2 points

* Midpoint of the two points

* Distance between the 2 points

* 2 remaining angles of the rignt triangle formed by the 2 points

* y intercept of the line equation

* Point-Slope Form

* Parametric Equations and Symmetric Equations

Or, if you are given a point on a line and the slope of the line including that point, this calculates the equation of that line and the y intercept of that line equation, and point-slope form.

Also allows for the entry of m and b to form the line equation

* Slope of the line (rise over run) and the line equation y = mx + b that joins the 2 points

* Midpoint of the two points

* Distance between the 2 points

* 2 remaining angles of the rignt triangle formed by the 2 points

* y intercept of the line equation

* Point-Slope Form

* Parametric Equations and Symmetric Equations

Or, if you are given a point on a line and the slope of the line including that point, this calculates the equation of that line and the y intercept of that line equation, and point-slope form.

Also allows for the entry of m and b to form the line equation

n and m are congruent and supplementary. prove n and m are right angles

n and m are congruent and supplementary. prove n and m are right angles
Given:
[LIST]
[*]n and m are congruent
[*]n and m are supplementary
[/LIST]
If n and m are supplementary, that means we have the equation:
m + n = 180
We're also given n and m are congruent, meaning they are equal. So we can substitute n = m into the supplementary equation:
m + m = 180
To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm%3D180&pl=Solve']we type it in our search engine[/URL] and we get:
m = 90
This means m = 90, n = 90, which means they are both right angles since by definition, a right angle is 90 degrees.

Pascal-Floyd-Leibniz Triangle

This generates the first (n) rows of the following triangles:

Pascal's Triangle

Leibniz's Harmonic Triangle

Floyd's Triangle

Pascal's Triangle

Leibniz's Harmonic Triangle

Floyd's Triangle

Perimeter of a rectangle is 372 yards. If the length is 99 yards, what is the width?

Perimeter of a rectangle is 372 yards. If the length is 99 yards, what is the width?
The perimeter P of a rectangle with length l and width w is:
2l + 2w = P
We're given P = 372 and l = 99, so we have:
2(99) + 2w = 372
2w + 198 = 372
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 198 and 372. To do that, we subtract 198 from both sides
2w + 198 - 198 = 372 - 198
[SIZE=5][B]Step 2: Cancel 198 on the left side:[/B][/SIZE]
2w = 174
[SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE]
2w/2 = 174/2
w = [B]87[/B]

Polar Conics

Given eccentricity (e), directrix (d), and angle θ, this determines the vertical and horizontal directrix polar equations.

Polygon Side

Determines the sides of a polygon given an interior angle sum.

Polygons

Using various input scenarios of a polygon such as side length, number of sides, apothem, and radius, this calculator determines Perimeter or a polygon and Area of the polygon.
This also determines interior angles of a polygon and diagonals of a polygon as well as the total number of 1 vertex diagonals.

Put the number 123456789 exactly ones in the bubble so that each edge adds up to say number

Put the number 123456789 exactly ones in the bubble so that each edge adds up to say number
[B]
Each side adds up to 17
[IMG]https://www.mathcelebrity.com/images/triangle_sum_17.png[/IMG]
[/B]

Pythagorean Theorem

Figures out based on user entry the missing side or missing hypotenuse of a right triangle. In addition, the calculator shows the proof of the Pythagorean Theorem and then determines by numerical evaluation if the 2 sides and hypotenuse you entered are a right triangle using the Pythagorean Theorem

Pythagorean Theorem Trig Proofs

Shows the proof of 3 pythagorean theorem related identities using the angle θ:

Sin^{2}(θ) + Cos^{2}(θ) = 1

Tan^{2}(θ) + 1 = Sec^{2}(θ)

Sin(θ)/Cos(θ) = Tan(θ)

Sin

Tan

Sin(θ)/Cos(θ) = Tan(θ)

Quadrilateral

Given 4 points entered, this determines the area using Brahmaguptas Formula and perimeter of the quadrilateral formed by the points as well as checking to see if the quadrilateral (quadrangle) is a parallelogram.

rectangle abcd prove: triangle adc is congruent to triangle bcd

rectangle abcd prove: triangle adc is congruent to triangle bcd
1. Given: ABCD is a rectangle
2. AB = CD since opposite sides of rectangle are congruent
3. BC = AD since opposite sides of rectangle are congruent
4. AC = AC by the Reflexive Property of Equality
5. triangle ADC = triangle CBA by the Side-Side-Side (SSS) Property

Rectangles and Parallelograms

Solve for Area, Perimeter, length, and width of a rectangle or parallelogram and also calculates the diagonal length as well as the circumradius and inradius.

Reference Angle

Calculates the reference angle for a given angle. Also known as the positive acute angle.

Right Triangles

This solves for all the pieces of a right triangle based on given inputs using items like the sin ratio, cosine ratio, tangent ratio, and the Pythagorean Theorem as well as the inradius.

Running from the top of a flagpole to a hook in the ground there is a rope that is 9 meters long. If

Running from the top of a flagpole to a hook in the ground there is a rope that is 9 meters long. If the hook is 4 meters from the base of the flagpole, how tall is the flagpole?
We have a right triangle, with hypotenuse of 9 and side of 4.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=4&hypinput=9&pl=Solve+Missing+Side']Using our Pythagorean Theorem calculator[/URL], we get a flagpole height of [B]8.063[/B].

Sam leaves school to go home. He walks 10 blocks North and then 8 blocks west. How far is John from

Sam leaves school to go home. He walks 10 blocks North and then 8 blocks west. How far is John from the school?
Sam walked at a right angle. His distance from home to school is the hypotenuse.
Using our [URL='https://www.mathcelebrity.com/pythag.php?side1input=8&side2input=10&hypinput=&pl=Solve+Missing+Side']Pythagorean theorem calculator[/URL], we get:
[B]12.806 blocks[/B]

Solve for x

[IMG]https://mathcelebrity.com/community/data/attachments/0/supp-angles.jpg[/IMG]
The angle with measurements of 148 degrees lies on a straight line, which means it's supplementanry angle is:
180 - 148 = 32
Since the angle of 2x - 16 and 32 lie on a straight line, their angle sum equals 180:
2x + 16 + 32 = 180
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B16%2B32%3D180&pl=Solve']type it in our math engine [/URL]and we get:
x = [B]66[/B]

Special Triangles: Isosceles and 30-60-90

Given an Isosceles triangle (45-45-90) or 30-60-90 right triangle, the calculator will solve the 2 remaining sides of the triangle given one side entered.

Sum to Product and Product to Sum Formulas

Given two angles in degrees of u and v, this determines the following:

* Sin(u) ± Sin(v)

* Cos(u) ± Cos(v)

* Sin(u)Sin(v)

* Cos(u)Cos(v)

* Sin(u)Cos(v)

* Cos(u)Sin(v)

* Sin(u + v)

* Sin(u - v)

* Cos(u + v)

* Cos(u - v)

* Tan(u + v)

* Tan(u - v)

* Sin(u) ± Sin(v)

* Cos(u) ± Cos(v)

* Sin(u)Sin(v)

* Cos(u)Cos(v)

* Sin(u)Cos(v)

* Cos(u)Sin(v)

* Sin(u + v)

* Sin(u - v)

* Cos(u + v)

* Cos(u - v)

* Tan(u + v)

* Tan(u - v)

The base of a triangle with a height of 7 units is represented by the formula b=2/7A. The base of th

The base of a triangle with a height of 7 units is represented by the formula b=2/7A. The base of the triangle is less than 10 units. Write and solve an inequality that represents the possible area A of the triangle
We're given:
b=2/7A
We're also told that b is less than 10. So we have:
2/7A < 10
2A/7 < 10
Cross multiply:
2A < 7 * 10
2A < 70
Divide each side of the inequality by 2 to isolate A
2A/2 < 70/2
Cancel the 2's on the left side and we get:
A < [B]35[/B]

The circle has an arc measure of 180 degrees

The circle has an arc measure of 180 degrees - True or False.
False. A Circle has an arc measure of 360 degrees.
A few vital facts about arcs measures, also called central angles:
[LIST=1]
[*]An arc measure [I]< [/I]180° is a minor arc.
[*]An arc measure [I]> [/I]180° is a major arc.
[*]An arc measure [I]= [/I]180° is a semicircle.
[*]An arc measure [I]= 36[/I]0° is a circle.
[/LIST]

The dimensions of a rectangle are 30 cm and 18 cm. When its length decreased by x cm and its width i

The dimensions of a rectangle are 30 cm and 18 cm. When its length decreased
by x cm and its width is increased by x cm, its area is increased by 35 sq. cm.
a. Express the new length and the new width in terms of x.
b. Express the new area of the rectangle in terms of x.
c. Find the value of x.
Calculate the current area. Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=30&w=18&a=&p=&pl=Calculate+Rectangle']rectangle calculator with length = 30 and width = 18[/URL], we get:
A = 540
a) Decrease length by x and increase width by x, and we get:
[LIST]
[*]length = [B]30 - x[/B]
[*]width = [B]18 + x[/B]
[/LIST]
b) Our new area using the lw = A formula is:
(30 - x)(18 + x) = 540 + 35
Multiplying through and simplifying, we get:
540 - 18x + 30x - x^2 = 575
[B]-x^2 + 12x + 540 = 575[/B]
c) We have a quadratic equation. To solve this, [URL='https://www.mathcelebrity.com/quadratic.php?num=-x%5E2%2B12x%2B540%3D575&pl=Solve+Quadratic+Equation&hintnum=+0']we type it in our search engine, choose solve[/URL], and we get:
[B]x = 5 or x = 7[/B]
Trying x = 5, we get:
A = (30 - 5)(18 + 5)
A = 25 * 23
A = 575
Now let's try x = 7:
A = (30 - 7)(18 + 7)
A = 23 * 25
A = 575
They both check out.
So we can have

The distance between consecutive bases is 90 feet. An outfielder catches the ball on the third base

The distance between consecutive bases is 90 feet. An outfielder catches the ball on the third base line about 40 feet behind third base. How far would the outfielder have to throw the ball to first base?
We have a right triangle. From home base to third base is 90 feet. We add another 40 feet to the outfielder behind third base to get: 90 + 40 = 130
The distance from home to first is 90 feet.
Our hypotenuse is the distance from the outfielder to first base.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=130&side2input=90&hypinput=&pl=Solve+Missing+Side']Using our Pythagorean theorem calculator[/URL], we get:
d = [B]158.11 feet[/B]

The largest American flag ever flown had a perimeter of 1,520 feet and a length of 505 feet. Find th

The largest American flag ever flown had a perimeter of 1,520 feet and a length of 505 feet. Find the width of the flag.
for a rectangle, the Perimeter P is given by:
P = 2l + 2w
P[URL='https://www.mathcelebrity.com/rectangle.php?l=505&w=&a=&p=1520&pl=Calculate+Rectangle']lugging in our numbers for Perimeter and width into our rectangle calculator[/URL], we get:
l =[B] 255[/B]

The length of a rectangle is equal to triple the width. Find the length of the rectangle if the peri

The length of a rectangle is equal to triple the width. Find the length of the rectangle if the perimeter is 80 inches.
The perimeter (P) of a rectangle is:
2l + 2w = P
We're given two equations:
[LIST=1]
[*]l = 3w
[*]2l + 2w = 80
[/LIST]
We substitute equation 1 into equation 2 for l:
2(3w) + 2w = 80
6w + 2w = 80
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D80&pl=Solve']type it in our search engine[/URL] and we get:
w = 10
To solve for the length (l), we substitute w = 10 into equation 1 above:
l = 3(10)
l = [B]30[/B]

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 fee

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building.
Using our [URL='http://www.mathcelebrity.com/rectangle-word-problems.php?t1=perimeter&v1=120&t2=length&v2=6&op=less&v3=3&t4=times&t5=width&pl=Calculate']rectangular word problem calculator[/URL], we have:
[LIST]
[*][B]l = 43.5[/B]
[*][B]w = 16.5[/B]
[/LIST]

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 fee

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building.
Using our [URL='http://www.mathcelebrity.com/rectangle-word-problems.php?t1=perimeter&v1=120&t2=length&v2=6&op=less&v3=3&t4=times&t5=width&pl=Calculate']rectangle word problem calculator[/URL], we get:
[LIST]
[*][B]w = 16.5[/B]
[*][B]l = 43.5[/B]
[/LIST]

the length of a rectangular map is 15 inches and the perimeter is 50 inches. Find the width

The length of a rectangular map is 15 inches and the perimeter is 50 inches. Find the width.
Using our r[URL='http://www.mathcelebrity.com/rectangle.php?l=3&w=&a=&p=50&pl=Calculate+Rectangle']ectangle solver[/URL], we get [B]w = 10[/B].

The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft²

The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft²
The frame is a rectangle. The area of a rectangle is A = lw. So were given:
[LIST=1]
[*]l = w + 1
[*]lw = 12
[/LIST]
Substitute equation (1) into equation (2) for l:
(w + 1) * w = 12
Multiply through and simplify:
w^2 + w = 12
We have a quadratic equation. To solve for w, we type this equation into our search engine and we get two solutions:
w = 3
w = -4
Since width cannot be negative, we choose the positive result and have:
w = [B]3[/B]
To solve for length, we plug w = 3 into equation (1) above and get:
l = 3 + 1
l = [B]4[/B]

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters. Find the dimensions of Sally’s garden.
Gardens have a rectangle shape. Perimeter of a rectangle is 2l + 2w. We're given:
[LIST=1]
[*]l = 3w + 4 [I](3 times the width Plus 4 since greater means add)[/I]
[*]2l + 2w = 72
[/LIST]
We substitute equation (1) into equation (2) for l:
2(3w + 4) + 2w = 72
Multiply through and simplify:
6w + 8 + 2w = 72
(6 +2)w + 8 = 72
8w + 8 = 72
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=8w%2B8%3D72&pl=Solve']type it in our search engine[/URL] and we get:
w = [B]8
[/B]
To solve for l, we substitute w = 8 above into Equation (1):
l = 3(8) + 4
l = 24 + 4
l = [B]28[/B]

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters
A garden is a rectangle, which has perimeter P of:
P = 2l + 2w
With P = 72, we have:
2l + 2w = 72
We're also given:
l = 3w + 4
We substitute this into the perimeter equation for l:
2(3w + 4) + 2w = 72
6w + 8 + 2w = 72
To solve this equation for w, we t[URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B8%2B2w%3D72&pl=Solve']ype it in our search engine[/URL] and we get:
w =[B] 8[/B]
Now, to solve for l, we substitute w = 8 into our length equation above:
l = 3(8) + 4
l = 24 + 4
l = [B]28[/B]

The length of the flag is 2 cm less than 7 times the width. The perimeter is 60cm. Find the length a

The length of the flag is 2 cm less than 7 times the width. The perimeter is 60cm. Find the length and width.
A flag is a rectangle shape. So we have the following equations
Since P = 2l + 2w, we have 2l + 2w = 60
l = 7w - 2
Substitute Equation 1 into Equation 2:
2(7w -2) + 2w = 60
14w - 4 + 2w = 60
16w - 4 = 60
Add 4 to each side
16w = 64
Divide each side by 16 to isolate w
w = 4
Which means l = 7(4) - 2 = 28 - 2 = 26

The perimeter of a bedroom door is 28 feet. It is 4 feet wide. How tall is it?

The perimeter of a bedroom door is 28 feet. It is 4 feet wide. How tall is it?
Using our[URL='https://www.mathcelebrity.com/rectangle.php?l=&w=4&a=&p=28&pl=Calculate+Rectangle'] rectangle calculator[/URL], we get:
l = [B]10[/B]

The perimeter of a college basketball court is 102 meters and the length is twice as long as the wid

The perimeter of a college basketball court is 102 meters and the length is twice as long as the width. What are the length and width?
A basketball court is a rectangle. The perimeter P is:
P = 2l + 2w
We're also given l = 2w and P = 102. Plug these into the perimeter formula:
2(2w) + 2w = 102
4w + 2w = 102
6w = 102
[URL='https://www.mathcelebrity.com/1unk.php?num=6w%3D102&pl=Solve']Typing this equation into our calculator[/URL], we get:
[B]w = 17[/B]
Plug this into the l = 2w formula, we get:
l = 2(17)
[B]l = 34[/B]

The perimeter of a poster is 20 feet. The poster is 6 feet tall. How wide is it?

The perimeter of a poster is 20 feet. The poster is 6 feet tall. How wide is it?
[U]Assumptions and givens:[/U]
[LIST]
[*]The poster has a rectangle shape
[*]l = 6
[*]P = 20
[*]The perimeter of a rectangle (P) is: 2l + 2w = P
[/LIST]
Plugging in our l and P values, we get:
2(6) + 2w = 20
Multiplying through and simplifying, we get:
12 + 2w = 20
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=12%2B2w%3D20&pl=Solve']type this equation into our search engine [/URL]and we get:
w = [B]4[/B]

The perimeter of a rectangle is 400 meters. The length is 15 meters less than 4 times the width. Fin

The perimeter of a rectangle is 400 meters. The length is 15 meters less than 4 times the width. Find the length and the width of the rectangle.
l = 4w - 15
Perimeter = 2l + 2w
Substitute, we get:
400 = 2(4w - 15) + 2w
400 = 8w - 30 + 2w
10w - 30 = 400
Add 30 to each side
10w = 370
Divide each side by 10 to isolate w
w = 37
Plug that back into our original equation to find l
l = 4(37) - 15
l = 148 - 15
l = 133
So we have (l, w) = (37, 133)

The perimeter of a rectangle parking lot is 340 m. If the length of the parking lot is 97 m, what is

The perimeter of a rectangle parking lot is 340 m. If the length of the parking lot is 97 m, what is it’s width?
The formula for a rectangles perimeter P, is:
P = 2l + 2w where l is the length and w is the width.
Plugging in our P = 340 and l = 97, we have:
2(97) + 2w = 340
Multiply through, we get:
2w + 194 = 340
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B194%3D340&pl=Solve']Type this equation into our search engine[/URL], we get:
[B]w = 73[/B]

The perimeter of a rectangular backyard is 162 feet. It is 52 feet long. How wide is it?

The perimeter of a rectangular backyard is 162 feet. It is 52 feet long. How wide is it?
We [URL='https://www.mathcelebrity.com/rectangle.php?l=52&w=&a=&p=162&pl=Calculate+Rectangle']use our rectangle solver to solve for w[/URL]. We get:
[B]w = 29[/B]

The perimeter of a rectangular field is 250 yards. If the length of the field is 69 yards, what is

The perimeter of a rectangular field is 250 yards. If the length of the field is 69 yards, what is its width?
Set up the rectangle perimeter equation:
P = 2l + 2w
For l = 69 and P = 250, we have:
250= 2(69) + 2w
250 = 138 + 2w
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2w%2B138%3D250&pl=Solve']equation solver[/URL], we get:
[B]w = 56 [/B]

The perimeter of a rectangular field is 300m. If the width of the field is 59m, what is it’s length

The perimeter of a rectangular field is 300m. If the width of the field is 59m, what is it’s length?
Set up the perimeter (P) of a rectangle equation given length (l) and width (w):
2l + 2w = P
We're given P = 300 and w = 59. Plug these into the perimeter equation:
2l + 2(59) = 300
2l + 118 = 300
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B118%3D300&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]l = 91[/B]

The perimeter of a rectangular notecard is 16 inches. The notecard is 5 inches wide. How tall is it?

The perimeter of a rectangular notecard is 16 inches. The notecard is 5 inches wide. How tall is it?
Perimeter of a rectangle P is:
P = 2l + 2w
We have:
2l + 2w = 16
We are given w = 5, so we have:
2l + 2(5) = 16
2l + 10 = 16
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B10%3D16&pl=Solve']Plugging this into our equation calculator[/URL], we get [B]l = 3[/B].

The perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. Wh

The perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. What are the dimensions of the patio?
Perimeter of a rectangle is:
P = 2l + 2w
We're given l = w + 3 and P = 54. So plug this into our perimeter formula:
54= 2(w + 3) + 2w
54 = 2w + 6 + 2w
Combine like terms:
4w + 6 = 54
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B6%3D54&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 12[/B]
Plug this into our l = w + 3 formula:
l = 12 + 3
[B]l = 15[/B]

The perimeter of a rectangular parking lot is 258 meters. If the length of the parking lot is 71, wh

The perimeter of a rectangular parking lot is 258 meters. If the length of the parking lot is 71, what is its width?
The perimeter for a rectangle (P) is given as:
2l + 2w = P
We're given P = 258 and l = 71. Plug these values in:
2(71) + 2w = 258
142 + 2w = 258
[URL='https://www.mathcelebrity.com/1unk.php?num=142%2B2w%3D258&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 58[/B]

The perimeter of a rectangular shelf is 60 inches. The shelf is 7 inches deep. How wide is it?

The perimeter of a rectangular shelf is 60 inches. The shelf is 7 inches deep. How wide is it?
The perimeter for a rectangle is given below:
P = 2l + 2w
We're given l = 7 and P = 60. Plug this into the perimeter formula:
60 = 2(7) + 2w
60 = 14 + 2w
Rewritten, it's 2w + 14 = 60.
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B14%3D60&pl=Solve']Typing this equation into our search engine[/URL], we get [B]w = 23[/B].

The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimete

The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimeter of the triangle if its area is 3000.
[LIST]
[*]h = b + 70
[*]A = 1/2bh = 3000
[/LIST]
Substitute the height equation into the area equation
1/2b(b + 70) = 3000
Multiply each side by 2
b^2 + 70b = 6000
Subtract 6000 from each side:
b^2 + 70b - 6000 = 0
Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=b%5E2%2B70b-6000%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get:
b = 50 and b = -120
Since the base cannot be negative, we use b = 50.
If b = 50, then h = 50 + 70 = 120
The perimeter is b + h + hypotenuse
Using the [URL='http://www.mathcelebrity.com/righttriangle.php?angle_a=&a=70&angle_b=&b=50&c=&pl=Calculate+Right+Triangle']right-triangle calculator[/URL], we get hypotenuse = 86.02
Adding up all 3 for the perimeter: 50 + 70 + 86.02 = [B]206.02[/B]

The sides of a triangle are consecutive numbers. If the perimeter of the triangle is 240 m, find the

The sides of a triangle are consecutive numbers. If the perimeter of the triangle is 240 m, find the length of each side
Let the first side be n.
Next side which is consecutive is n + 1
Next side which is consecutive is n + 1 + 1 = n + 2
So we have the sum of 3 consecutive numbers is 240.
We type in [I][URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof3consecutivenumbersis240&pl=Calculate']sum of 3 consecutive numbers is 240[/URL][/I] into our search engine and we get:
[B]79, 80, 81[/B]

The sum of the measures of two exterior angles of a triangle is 205. What is the measure of the thir

The sum of the measures of two exterior angles of a triangle is 205. What is the measure of the third exterior angle?
The sum of exterior angles for a triangle is 360.
To find the third exterior angle, we take 360 - 205 = [B]155[/B].

The width of a rectangle is fixed at 4cm. For what lengths will the area be less than 86 cm^2

The width of a rectangle is fixed at 4cm. For what lengths will the area be less than 86 cm^2
The Area (A) of a rectangle is given by:
A = lw
With an area of [I]less than[/I] 86 and a width of 4, we have the following inequality:
4l < 86
To solve for l, we [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=4l%3C86&pl=Show+Interval+Notation']type this inequality into our search engine[/URL] and we get:
[B]l < 21.5[/B]

There is an escalator that is 1090.3 feet long and drops a vertical distance of 193.4 feet. What is

There is an escalator that is 1090.3 feet long and drops a vertical distance of 193.4 feet. What is its angle of depression?
The sin of the angle A is the length of the opposite side / hypotenuse.
sin(A) = Opposite / Hypotenuse
sin(A) = 193.4 / 1090/3
sin(A) = 0.1774
[URL='https://www.mathcelebrity.com/anglebasic.php?entry=0.1774&pl=arcsin']We want the arcsin(0.1774)[/URL].
[B]A = 10.1284[/B]

Triangle Coordinate Items

Enter 3 points for the vertices of a triangle, and this will calculate the area of that triangle and the centroid.

Triangle Inequality

This calculator displays 2 scenarios

1) Enter 3 sides of a triangle, and it will determine if the side lengths satisfy the properties of the triangle inequality and form a triangle

2) Enter 2 sides of a triangle, and this will determine an acceptable range for the length of the 3rd side of a triangle so that the 3rd side respects the Triangle Inequality.

1) Enter 3 sides of a triangle, and it will determine if the side lengths satisfy the properties of the triangle inequality and form a triangle

2) Enter 2 sides of a triangle, and this will determine an acceptable range for the length of the 3rd side of a triangle so that the 3rd side respects the Triangle Inequality.

Triangle KLM has vertices at . k(-2,-2), l(10,-2), m(4,4) What type of triangle is KLM?

Triangle KLM has vertices at . k(-2,-2), l(10,-2), m(4,4) What type of triangle is KLM?
[URL='https://www.mathcelebrity.com/slope.php?xone=-2&yone=-2&slope=+2%2F5&xtwo=10&ytwo=-2&pl=You+entered+2+points']Side 1: KL[/URL] = 12
[URL='https://www.mathcelebrity.com/slope.php?xone=10&yone=-2&slope=+2%2F5&xtwo=4&ytwo=4&pl=You+entered+2+points']Side 2: LM[/URL] = 8.4853
[URL='https://www.mathcelebrity.com/slope.php?xone=-2&yone=2&slope=+2%2F5&xtwo=4&ytwo=4&pl=You+entered+2+points']Side 3: KM[/URL] = 6.3246
Then, we want to find the type of triangle. Using our [URL='https://www.mathcelebrity.com/tribasic.php?side1input=12&side2input=8.4853&side3input=6.3246&angle1input=&angle2input=&angle3input=&pl=Solve+Triangle']triangle solver with our 3 sides[/URL], we get:
[B]Obtuse, Scalene[/B]

Triangle Solver and Classify Triangles

Solves a triangle including area using the following solving methods

Side-Angle-Side (SAS) Side Angle Side

Angle-Side-Angle (ASA) Angle Side Angle

Side-Side-Angle (SSA) Side Angle Side

Side-Side-Side (SSS) Side Side Side

Area (A) is solved using Herons Formula

Law of Sines

Law of Cosines

Also classifies triangles based on sides and angles entered.

Side-Angle-Side (SAS) Side Angle Side

Angle-Side-Angle (ASA) Angle Side Angle

Side-Side-Angle (SSA) Side Angle Side

Side-Side-Side (SSS) Side Side Side

Area (A) is solved using Herons Formula

Law of Sines

Law of Cosines

Also classifies triangles based on sides and angles entered.

triangle sum theorem

The triangle sum theorem states the sum of the three angles in a triangle equals 180 degrees.
So if you're given two angles and need too find the 3rd angle, add the 2 known angles up, and subtract them from 180 to get the 3rd angle measure.

Triangle with perimeter

A triangle with a perimeter of 120.
What degree are the three sides?

Triangle with perimeter

What kind of triangle? Do you have side lengths? I need more information.

Triangles

This lesson walks you through the basics of a triangle and shows you triangle types like acute, right, obtuse, scalene, isosceles, equilateral.

Trig Measurement

Given an angle θ, this calculates the following measurements:

Sin(θ) = Sine

Cos(θ) = Cosine

Tan(θ) = Tangent

Csc(θ) = Cosecant

Sec(θ) = Secant

Cot(θ) = Cotangent

Arcsin(x) = θ = Arcsine

Arccos(x) = θ = Arccosine

Arctan(x) =θ = Arctangent

Also converts between Degrees and Radians and Gradians

Coterminal Angles as well as determine if it is acute, obtuse, or right angle. For acute angles, a cofunction will be determined. Also shows the trigonometry function unit circle

Sin(θ) = Sine

Cos(θ) = Cosine

Tan(θ) = Tangent

Csc(θ) = Cosecant

Sec(θ) = Secant

Cot(θ) = Cotangent

Arcsin(x) = θ = Arcsine

Arccos(x) = θ = Arccosine

Arctan(x) =θ = Arctangent

Also converts between Degrees and Radians and Gradians

Coterminal Angles as well as determine if it is acute, obtuse, or right angle. For acute angles, a cofunction will be determined. Also shows the trigonometry function unit circle

Trigonometry Summary

This is a list of important angle formulas and identities in trigonometry

Tristan is building a slide for his kids. The ladder is 6 feet tall and the slide is 10 feet long. W

Tristan is building a slide for his kids. The ladder is 6 feet tall and the slide is 10 feet long. What is the distance between the ladder and the bottom of the slide?
The answer is 8.
We have a 3-4-5 triangle. But it's scaled by 2.
3 * 2 = 6
5 * 2 = 10 (hypotenuse-slide)
4 * 2 = [B]8[/B]

Vectors

Given 2 vectors A and B, this calculates:

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj_{B}A and and the vector component of A orthogonal to B → A - proj_{B}A

Also calculates the horizontal component and vertical component of a 2-D vector.

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj

Also calculates the horizontal component and vertical component of a 2-D vector.

What is a Perpendicular Bisector

This lesson walks you through what a perpendicular bisector is and the various properties of the segment it bisects and the angles formed by the bisection

What is an Angle

This lesson walks you through what an angle is and how to use it

What is the area of a triangular parking lot with a width of 200m and a length of 100m?What is the a

What is the area of a triangular parking lot with a width of 200m and a length of 100m?
Area of a Triangle = bh/2
Plugging in our numbers, we get:
Area of Parking Lot = 200(100)/2
Area of Parking Lot = 100 * 100
Area of Parking Lot = [B]10,000 sq meters[/B]