## An elementary proof of the cosine law

The cosine law states that in triangle $ABC$ with side lengths $a, b,$ and $c$, the following equations are satisfied:

$a ^2 = b^2 + c^2 - 2bc$ $\cos A$*

$b ^2 = a^2 + c^2 - 2ac$ $\cos B$

$c ^2 = a^2 + b^2 - 2ab$ $\cos C$

The discussion below shows how these equations were derived. » Read more