Question

Use the law of cosines to explain why c^2=a^2+b^2 for triangle ABC, where angle C is a right angle.

Answer 1

Let $c$ be the length of the hypotenuse in the right triangle $ABC$, with $m\angle C=90^\circ$ for $\angle C$, the angle opposite the hypotenuse.

By the law of cosines,

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

But $\cos90^\circ=0$, so we end up with $c^2=a^2+b^2$.