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

1 Answer
David G.
Apr 2, 2018

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?

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