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

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.