Use the image to answer the 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
Yes, because it is a right triangle.
Yes, because it is a right triangle.
No, because the triangle is not a right triangle.
No, because the triangle is not a right triangle.
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
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Yes, because it is a right triangle. You can determine this because angle E measures 60 degrees and angle D measures 30 degrees, making angle F a right angle (90 degrees).
The correct answer is:
No, because the triangle is not a right triangle.
We know this because the angles at points E and D are given as 60 degrees and 30 degrees respectively, indicating that this triangle is an acute triangle, not a right triangle.
To determine whether the Pythagorean Theorem applies to this triangle, we need to check if it is a right triangle. A right triangle is one that has one angle measuring 90 degrees. In this case, the question states that angle E measures 60 degrees and angle D measures 30 degrees. However, it does not mention the angle at point F.
To find out if the triangle is a right triangle, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Since angle E measures 60 degrees and angle D measures 30 degrees, we can calculate the measure of angle F by subtracting the sum of angle E and angle D from 180 degrees.
180 - (60 + 30) = 180 - 90 = 90 degrees
Therefore, angle F measures 90 degrees.
Since the triangle has a right angle (angle F is 90 degrees), the Pythagorean Theorem does apply to this triangle. We can verify this theorem by checking if the square of the length of the hypotenuse (25^2) is equal to the sum of the squares of the lengths of the other two sides (15^2 + 20^2).
25^2 = 625
15^2 + 20^2 = 225 + 400 = 625
Since both sides are equal, the Pythagorean Theorem is applicable to this triangle. Therefore, the correct answer is:
Yes, because it is a right triangle.