Which triangle is a right triangle?

To determine which triangle is a right triangle, we can use the converse of the Pythagorean theorem: If a² + b² = c², then the triangle is a right triangle, where c is the longest side.

Let’s check each set of side lengths:

1. 15, 8, 17:

( 15² + 8² = 225 + 64 = 289 )

( 17² = 289 )

Since ( 15² + 8² = 17² ), this is a right triangle.

2. 15, 16, 17:

( 15² + 16² = 225 + 256 = 481 )

( 17² = 289 )

Since ( 15² + 16² neq 17² ), this is not a right triangle.

3. 15, 8, 9:

( 15² + 8² = 225 + 64 = 289 )

( 9² = 81 )

Since ( 15² + 8² neq 9² ), this is not a right triangle.

Conclusion: The triangle with sides 15, 8, and 17 is a right triangle.