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

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Answer:

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.

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