Question

A triangle has sides of lengths 4, 3, and 5 is it a right triangle?

Answer 1

Yes, it is.

Explanation:

Use the Pythagorean Rule to check;

`5^2 = 3^3 + 4^2`
25 = 9 + 16 . OK

Answer 2

Let's see. Let's use the Law of Cosines to check by solving for an angle or two.

`c^2 = a^2 + b^2 - 2ab*cosC`

`5^2 = 3^2 + 4^2 - 2(3)(4)*cosC`

`0 = - 2(3)(4)*cosC`

`0 = cosC`

`C = 90^o, cancel(270^o)`

Therefore, with `C = 90^o` as one of the angles, it is a right triangle.