Question

A triangle has the vertices labeled upper E upper F upper D. The height upper E upper F is labeled 15, the base upper D upper F is labeled 20, and the hypotenuse upper D upper E is labeled 25. Angle upper E measures 60 degrees and angle upper D measures 30 degrees.
Does the Pythagorean Theorem apply to this triangle? How do you know?
A. Yes, because you can use the Pythagorean Theorem on any triangle
B. Yes, because it is a right triangle.
C. No, because the triangle is not a right triangle.
D. No, because the angle at point F is 90°.

Answer 1

B. Yes, because it is a right triangle.

Reason: 15^2 + 20^2 = 225 + 400 = 625 = 25^2, so the sides satisfy the Pythagorean relation. Also angles E = 60° and D = 30° imply angle F = 180° − 60° − 30° = 90°, so the triangle is right-angled at F.