Solving a Triangle From Its Sides

Given all three sides (SSS), everything else follows: area by Heron's formula, angles by the Law of Cosines, perimeter by summation, and heights from 2A ÷ side. This calculator solves the complete triangle from three side lengths.

The Law of Cosines

For sides a, b, c: cos C = (a² + b² − c²) ÷ 2ab. It generalizes the Pythagorean theorem to every triangle — when C = 90°, the cosine term vanishes and you recover a² + b² = c² exactly.

Heron's Formula

Heron's formula, area = √(s(s−a)(s−b)(s−c)) with s = perimeter ÷ 2, computes area from sides alone — no trigonometry required. It works for every triangle, including scalene and obtuse ones.