Law of Cosines for an angle: cos A = (b² + c² − a²)/(2bc)

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

oblique

Related Law of Cosines identities

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.

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.