Proof of Cosine Rule

The Law of Cosines

The Law of Cosines states that given any triangle with side lengths a, b and c and opposing angles A, B and C is such that :

First we divide the triangle into two right triangles by drawing the line that passes through B and is perpendicular to b.

         

Now we have a right triangle with c as the hypotenuse. And so according to the Pythagorean Theorem