Law of cosines - Aetherwisp

The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides $a$ , $b$ and $c$ , opposite respective angles $\alpha$ , $\beta$ and $\gamma$ , we have

\begin{align} c^{2} & =a^{2}+b^{2}-2ab\cos \gamma \\ a^{2} & =b^{2}+c^{2}-2bc\cos \alpha \\ b^{2} & =a^{2}+c^{2}-2ac\cos \beta \end{align}

For a right triangle, where $\gamma=0$ , this reduces to the Pythagorean theorem: $c^{2}=a^{2}+b^{2}$ .