se the image to answer the question.

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?

(1 point)
Responses

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

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 triangle is not a right triangle.

Answer 1

To determine whether the Pythagorean Theorem applies to a triangle, we need to check if the triangle has a right angle. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we have the angles of the triangle: Angle E is 60 degrees, Angle D is 30 degrees, and Angle F must be 90 degrees (since the sum of angles in any triangle is 180 degrees and \(60 + 30 + 90 = 180\)).

Therefore, the triangle has a right angle at point F. Hence, it is a right triangle.

The correct response is:

Yes, because it is a right triangle.