To find out, we compare the triangle to a right triangle
whose legs are the same lengths as the two shorter sides.
We calculate its hypotenuse.  

If the hypotenuse is longer than the longest side, the triangle is acute.
If the hypotenuse is shorter than the longest side, the triangle is obtuse.
[If the hypotenuse is the same length as the longest side, the triangle is that
very right triangle.]

For a given triangle vith side lengths 6, 8, and 9, we find the hypotenuse 
of a right triangle with legs of length 6 and 8.

c² = a² + b²
c² = 6² + 8²
c² = 36 + 64
c² = 100
c = 
c = 10

Since the hypotenuse c=10 is longer than the third side of the give triangle,
9, the given triangle is acute.

Let's draw it to scale and see how it looks:



Sure looks acute to me!


Edwin