Question

The sides of a triangle are 30, 64, and 90. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.

Answer 1

Order sides: 30, 64, 90 (largest is 90). Compute squares:
90^2 = 8100, 30^2 + 64^2 = 900 + 4096 = 4996.

Since 90^2 > 30^2 + 64^2, the angle opposite the longest side is greater than 90°, so the triangle is obtuse.