Question

Show that the cosine law simplifies to the Pythagorean theorem when the contained angle between the two known sides is 90°.

Answer 1

See Below.

Explanation:

We want to show that the Law of Cosines simplifies to the Pythagorean Theorem when the contained angle between the two known sides is 90°.

The Law of Cosines is given by:

`c^2=a^2+b^2-2ab\cos(C)`

Where a and b are the two known sides, and C is the angle between them.

If C is 90° then we will have:

`c^2=a^2+b^2-2ab\cos(90 ^\circ)`

Recall that the cos(90°)=0. Hence:

`c^2=a^2+b^2-2ab(0)`

Simplify:

`c^2=a^2+b^2`

So, we acquire the Pythagorean Theorem as desired.