Triangle Calculator
Free triangle calculator. Solve triangles using SSS, SAS, ASA, or AAS methods. Calculate area, perimeter, angles, and side lengths with step-by-step solutions.
Angle C is the angle between sides a and b
Side c is between angles A and B
Side a is opposite angle A
Select a solve method and enter values to see the solution.
Our free triangle calculator solves triangles using SSS, SAS, ASA, or AAS methods. Calculate all sides, angles, area, and perimeter with detailed step-by-step explanations using the Law of Cosines and Law of Sines.
Triangle Solve Methods
SSS (Side-Side-Side)
Given all three sides, we can calculate all angles using the Law of Cosines:
cos(A) = (b² + c² - a²) / (2bc)
This method works for any valid triangle where the sum of any two sides is greater than the third.
SAS (Side-Angle-Side)
Given two sides and the included angle, we first find the third side using the Law of Cosines:
c² = a² + b² - 2ab·cos(C)
Then we use the Law of Sines to find the remaining angles.
ASA (Angle-Side-Angle)
Given two angles and the included side, we first find the third angle:
Angle C = 180° - A - B
Then we use the Law of Sines to find the remaining sides.
AAS (Angle-Angle-Side)
Given two angles and a non-included side, we first find the third angle, then use the Law of Sines to find the other sides. This is similar to ASA but the given side is opposite one of the known angles.
Key Formulas
| Formula | Description |
|---|---|
| Area = ½ab·sin(C) | Area from two sides and included angle |
| Area = √(s(s-a)(s-b)(s-c)) | Heron's formula, where s = (a+b+c)/2 |
| a/sin(A) = b/sin(B) = c/sin(C) | Law of Sines |
| c² = a² + b² - 2ab·cos(C) | Law of Cosines |
| A + B + C = 180° | Sum of angles in a triangle |
Triangle Types
- Equilateral: All sides equal, all angles 60°
- Isosceles: Two sides equal, two angles equal
- Scalene: All sides different, all angles different
- Right: One angle exactly 90°
- Acute: All angles less than 90°
- Obtuse: One angle greater than 90°