Law of Cosines for a side: a² = b² + c² − 2bc cos A

a^{2} = b^{2} + c^{2} - 2bc \cos A

a² = b² + c² − 2bc cos A finds the third side from two sides and the angle between them (SAS). It is the Pythagorean theorem with a correction term: when A = 90°, cos A = 0 and it collapses to a² = b² + c².

oblique

Related Law of Cosines identities

Solving for an angle

Practise it

Reading a formula is not the same as recalling it under time pressure. The workspace drills Law of Cosines questions in the quiz, and the triangle solver shows a worked solution for any triangle you type in.

Practise Law of Cosines Open the triangle solver

Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.