# The Cosine Law by Similarity

The Law of Cosines establishes a relationship between the angles and the side lengths of $\Delta ABC$:

$c^{2} = a^{2} + b^{2} - 2ab\cdot \mbox{cos}\gamma,$

where $\gamma$ is the angle in $\Delta ABC$ opposite side $c$.

This proof without words submitted by Anders Kaseorg combines together $3$ similar triangles; but where is the third? The proof was actually published at the American Mathematical Monthly, 121, February 2014, p 149, by Miles Dillon Edwards.

(There are several theorems that are proved by similar technique.)