The give side measures are 45, 60, 75.

Since the measure of the longest side is 36, So let c = 75, a = 45 and b = 60.

Then apply Pythagorean theorem: .

           (Substitute c = 75, a = 45 and b = 60)

Evaluate powers: .

Since , the triangle is a right triangle.

The measures , the triangle is a right triangle.