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`.