Cosine rule formula

The Cosine Rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

For a triangle with sides $a, b, c$ and angles $A, B, C$ opposite to those sides respectively:

To find a side:

$$a^2 = b^2 + c^2 - 2bc \cos(A)$$ $$b^2 = a^2 + c^2 - 2ac \cos(B)$$ $$c^2 = a^2 + b^2 - 2ab \cos(C)$$

To find an angle:

$$\cos(A) = \frac{b^2 + c^2 - a^2}{2bc}$$ $$\cos(B) = \frac{a^2 + c^2 - b^2}{2ac}$$ $$\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}$$