Question

How is the law of cosines related to the pythagorean theorem?

Answer 1

The Pythagorean Theorem can be stated as `a^2=b^2+c^2` (where `a` is the hypotenuse) and works only in right-angled triangles.

The Cosine Law is `a^2=b^2+c^2-2bc cosA` and works for all kinds of triangles.

Explanation:

The explanation is the really cool bit!

`A` in the cosine rule is the angle opposite to the side `a`.

Now, if `A=90^o` (which means the side opposite it, `a`, is the hypotenuse), we know that `cos 90^o=0`, so all the stuff after the minus sign in the Cosine Rule becomes `0`... and you will see that you just have the Pythagorean Theorem back again!

Because now you're working in a right-angled triangle.

Isn't that cool?