Question

The law of cosines can only be applied to nonright triangles. True of false.

Answer 1

false

Answer 2

Actually, the law of cosines for right triangles is a pretty cool thing to check out.

Answer 3

The law of cosines is:
c^2 = a^2 + b^2 - 2abCos(C)
Where C is the angle opposite from the side c. So let's see what happens when C is 90 degrees.

Answer 4

We get
c^2 = a^2 + b^2 -2abCos(90)

What is cos(90)? Well, it's 0. So this becomes:
c^2 = a^2 + b^2 - 2*ab*0
2*ab*0 = 0, so
c^2 = a^2 + b^2
which is the Pythagorean theorem! So the Pythagorean theorem which you have known for so long is actually a specific case of the law of cosines! Super cool! =D