Enter what you know below

<-- Side 1
<-- Side 2
<-- Side 3
<-- Angle 1
<-- Angle 2
<-- Angle 3
  

You entered 3 sides of a triangle.
Find the 3 angles using SSS method.

We need to check the largest angle first.
See if we have an obtuse angle
This is Side 3 Using Law of Cosines:

Find Angle 3 Using Law of Cosines

Take Arccosine of the following:
Angle 3  =  Side 12 + Side 22 - Side 32
  2 * Side 1 * Side 2

Angle 3  =  482 + 552 - 732
  2 * 48 * 55

Angle 3  =  2304 + 3025 - 5329
  5280

Angle 3  =  0
  5280

  Angle 3  =  Arccos(0)

  Angle 3  =  90°

Find Angle 2 Using Law of Cosines

Take Arccosine of the following:
Angle 2  =  Side 12 + Side 32 - Side 22
  2 * Side 1 * Side 3

Angle 2  =  482 + 732 - 552
  2 * 48 * 73

Angle 2  =  2304 + 5329 - 3025
  7008

Angle 2  =  4608
  7008

  Angle 2  =  Arccos(0.65753424657534)

  Angle 2  =  48.888°

Now solve for Angle 1
The sum of angles n a triangle = 180
Missing Angle = 180 - sum of 2 angles
Angle 1 = 180 - (Angle2 + Angle 3)
Angle 1 = 180 - (48.887909560833 + 90)
Angle 1 = 180 - 138.88790956083
Angle 1 = 41.112°

Calculate Semi-Permieter (s)

Use Heron's formula
s  =  Side1 + Side2 + Side3
  2

s  =  48 + 55 + 73
  2

s  =  176
  2

  s  =  88

Calculate Area (A)

Use Heron's formula
  A  =  √s * (s - side1) * (s - side2) * (s - side3)

  A  =  √88 * (88 - 48) * (88 - 55) * (88 - 73)

  A  =  √88 * (40) * (33) * (15)

  A  =  √1742400

  A  =  1320

Classify this triangle:

Since no sides equal each other
this is a Scalene Triangle
Since no sides equal each other
this is a Scalene Triangle



Keep Practicing
What is the Answer?
Since no sides equal each other
this is a Scalene Triangle
How does the Triangle Solver and Classify Triangles Calculator work?
Free Triangle Solver and Classify Triangles Calculator - 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.
This calculator has 1 input.

What 6 formulas are used for the Triangle Solver and Classify Triangles Calculator?

Acute Triangle = All angles < 90°
Right Triangle = One Angle = 90°
Obtuse Triangle = One angle > 90°
Equilateral Triangle = All sides equal
Isosceles Triangle = 2 sides equal
Scalene Triangle = No sides equal

For more math formulas, check out our Formula Dossier

What 6 concepts are covered in the Triangle Solver and Classify Triangles Calculator?

angle
the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
area
Number of square units covering the shape
heron
side
line segment joining two vertices in a polygon also known as an edge
triangle
a flat geometric figure that has three sides and three angles
triangle solver and classify triangles
Example calculations for the Triangle Solver and Classify Triangles Calculator

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