Triangle Calculator — Solve Any Triangle (Sides & Angles)
Solve any triangle by entering any valid combination of sides and angles. Uses Law of Sines and Law of Cosines. Shows area, perimeter, and triangle type.
Enter at least 3 values with at least 1 side. Angles are in degrees.
Examples:
Frequently Asked Questions
What information do I need to solve a triangle?
You need at least 3 pieces of information, with at least one being a side. Valid combinations are: SSS (3 sides), SAS (2 sides + included angle), ASA (2 angles + included side), AAS (2 angles + non-included side), SSA (2 sides + non-included angle — may have 0, 1, or 2 solutions).
What is the Law of Sines?
The Law of Sines states: a/sin(A) = b/sin(B) = c/sin(C). It is used when you know two angles and one side (AAS or ASA), or two sides and a non-included angle (SSA).
What is the Law of Cosines?
The Law of Cosines: c² = a² + b² - 2ab·cos(C). It generalizes the Pythagorean theorem and is used when you know three sides (SSS) or two sides and the included angle (SAS).
What types of triangles are there?
By sides: Equilateral (all sides equal), Isosceles (two sides equal), Scalene (all sides different). By angles: Acute (all angles < 90°), Right (one angle = 90°), Obtuse (one angle > 90°).
How is the area of a triangle calculated?
Several methods: (1) Area = (1/2) × base × height. (2) Heron's formula using all three sides: A = √(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2. (3) Area = (1/2)ab·sin(C) when two sides and the included angle are known.