Triangle Solver and Classify Triangles Calculator 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 1 Using Law of Cosines:

Find Angle 1 Using Law of Cosines

Take Arccosine of the following:

Angle 1  =	Side 22 + Side 32 - Side 12
	2 * Side 2 * Side 3

Angle 1  =	8.48532 + 6.32462 - 122
	2 * 8.4853 * 6.3246

Angle 1  =	72.00031609 + 40.00056516 - 144
	107.33225676

Angle 1  =	-31.99911875
	107.33225676

  Angle 1  =  Arccos(-0.29813142587276)

  Angle 1  =  107.345°

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  =	122 + 8.48532 - 6.32462
	2 * 12 * 8.4853

Angle 3  =	144 + 72.00031609 - 40.00056516
	203.6472

Angle 3  =	175.99975093
	203.6472

  Angle 3  =  Arccos(0.86423850133957)

  Angle 3  =  30.204°

Now solve for Angle 2
The sum of angles n a triangle = 180
Missing Angle = 180 - sum of 2 angles
Angle 2 = 180 - (Angle1 + Angle 3)
Angle 2 = 180 - (107.34540674467 + 30.20413451409)
Angle 2 = 180 - 137.54954125876
Angle 2 = 42.45°

Calculate Semi-Permieter (s)

Use Heron's formula

s  =	Side1 + Side2 + Side3
	2

s  =	12 + 8.4853 + 6.3246
	2

s  =	26.8099
	2

  s  =  13.405

Calculate Area (A)

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

  A  =  √13.405 * (13.405 - 12) * (13.405 - 8.4853) * (13.405 - 6.3246)

  A  =  √13.405 * (1.405) * (4.9197) * (7.0804)

  A  =  √656.05395287202

  A  =  25.614

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

You have 1 free calculations remaining

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?

anglethe figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. areaNumber of square units covering the shapeheronsideline segment joining two vertices in a polygon also known as an edgetrianglea flat geometric figure that has three sides and three anglestriangle solver and classify triangles

Example calculations for the Triangle Solver and Classify Triangles Calculator

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