Law of Cosines for a side: a² = b² + c² − 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.
Related Law of Cosines identities
Common questions
What is the Solving for a side identity?
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.
Which identities are related to Solving for a side?
Solving for a side belongs to the Law of Cosines group. The identities used alongside it most often are 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.
Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.