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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