Law of Cosines for an angle: cos A = (b² + c² − a²)/(2bc)
Rearranged for the angle, cos A = (b² + c² − a²)/(2bc) finds any angle from all three sides (SSS). Unlike the Law of Sines it has no ambiguous case: arccos returns a unique angle in [0, π], which is the whole range a triangle angle can occupy.
Related Law of Cosines identities
Common questions
What is the Solving for an angle identity?
Rearranged for the angle, cos A = (b² + c² − a²)/(2bc) finds any angle from all three sides (SSS). Unlike the Law of Sines it has no ambiguous case: arccos returns a unique angle in [0, π], which is the whole range a triangle angle can occupy.
Which identities are related to Solving for an angle?
Solving for an angle belongs to the Law of Cosines group. The identities used alongside it most often are Solving for a side.
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.