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.

Question

Does the Pythagorean Theorem apply to this triangle? How do you know?

(1 point)
Responses

No, because the triangle is not a right triangle.
No, because the triangle is not a right triangle.

Yes, because you can use the Pythagorean Theorem on any triangle
Yes, because you can use the Pythagorean Theorem on any triangle

Yes, because it is a right triangle.
Yes, because it is a right triangle.

No, because the angle at point F
is 90

Answer 1

The correct response is:

Yes, because it is a right triangle.

This triangle has angles measuring 60 degrees and 30 degrees, which implies that the third angle (at point F) is 90 degrees. Since there is a right angle in the triangle, the Pythagorean Theorem applies, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.