Question

What does the law of cosines reduce to when dealing with a right triangle

Answer 1

Pythagoras Theorem

Explanation:

For any triangle ABC, the law of cosine is given by

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

Now, let us suppose the triangle ABC is a right triangle having right angle at C.

Thus, C = 90°

Substituting this value in above formula

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

We know that cos 90°= 0

Thus, the equation becomes

`c^2=a^2+b^2-2ab\cdot0\\\\c^2=a^2+b^2`

We can see that it reduces to Pythagoras Theorem.

Hence, we can conclude that law of cosines reduce to Pythagoras Theorem when dealing with a right triangle