Question

A triangle has side lengths 9, 10, and 12. is it acute, obtuse, or right? explain.

Answer 1

Let "a", "b" and "с" be sides of the triangle ("с" is the longest side). The triangle will be:
right if a² + b² = c²
аcute if a² + b² > c²
obtuse if a² + b² < c²

We have a=9, b=10 and c=12

a² + b² = 9² + 10² = 81 + 100 = 181
and
c² = 12² = 144

181 > 144 ⇒ аcute triangle.