📏 Law of Cosines Calculator
Given two sides of a triangle and the angle between them, find the length of the third side and the triangle’s other two angles.
What the law of cosines does
The law of cosines relates the three sides of a triangle to one of its angles. It’s especially useful for “side-angle-side” triangles, where you know two sides and the angle between them but not the triangle’s third side, since regular right-triangle trigonometry doesn’t apply.
The formula used
Given sides a and b with included angle C, the third side is found with c² = a² + b² – 2ab·cos(C). Once all three sides are known, the remaining angles A and B are found by rearranging the same formula: cos(A) = (b² + c² – a²) / (2bc), and similarly for angle B.
This tool is intended for general math, geometry, and engineering learning purposes.