Final answer:
The triangle with side lengths 9, 12, and 15 is classified as an obtuse triangle.
Step-by-step explanation:
The lengths of the sides of a triangle are 9, 12, and 15.
To classify the triangle, we need to determine if it is acute, right, or obtuse.
In a triangle, the largest side is opposite the largest angle.
Using the Pythagorean theorem, we can determine that the square of the longest side, 15, is equal to the sum of the squares of the other two sides, 9 and 12.
15^2 = 9^2 + 12^2.
Since 15^2 is greater than 9^2 + 12^2, the triangle is obtuse.