Question

Jamel is asked to create triangles using three of four given sticks. The sticks measure 3 in., 6 in., 7 in., and 8 in. He creates these 4 triangles.

Triangle 1: 3 in., 6 in., 7 in.
Triangle 2: 3 in., 6 in., 8 in.
Triangle 3: 3 in., 7 in., 8 in.
Triangle 4: 6 in., 7 in., 8 in.

How many of his triangles are obtuse?

1
2
3
4

Answer 1

Use the largest side as c. A triangle is obtuse if c^2 > a^2 + b^2.

1) 3,6,7: 7^2 = 49, 3^2+6^2 = 9+36 = 45 → 49 > 45, obtuse.
2) 3,6,8: 8^2 = 64, 3^2+6^2 = 45 → 64 > 45, obtuse.
3) 3,7,8: 8^2 = 64, 3^2+7^2 = 9+49 = 58 → 64 > 58, obtuse.
4) 6,7,8: 8^2 = 64, 6^2+7^2 = 36+49 = 85 → 64 < 85, acute.

So 3 of the triangles are obtuse. Answer: 3.