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 angle at point F
is 90°
.
No, because the angle at point cap f is 90 degrees .

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

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

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

Answer 1

The correct response is:

No, because the triangle is not a right triangle.

To explain, the Pythagorean Theorem applies specifically to right triangles, where one of the angles is exactly 90 degrees. In this case, angles E and D measure 60 degrees and 30 degrees, respectively, which means that angle F must be 90 degrees (since the sum of angles in a triangle is 180 degrees). Therefore, this triangle does indeed have a right angle at point F, and the Pythagorean Theorem is applicable.

So, in this situation, it would actually be correct to say:

Yes, because it is a right triangle.

It seems there's a contradiction in your choices, as the triangle described has a right angle.