right triangle - triangle in which one angle is a right angle

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 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 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 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 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 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 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.

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]

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]

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]

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

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].

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.

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 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]

Triangles

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