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Angle e 60°

Angle d 30°
Angle f blank
The sides between f and e is 15
The sides between f and d 20

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

(1 point)

No, because the triangle is not a right triangle.

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

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

Yes, because it is a right triangle.

1 answer

To determine whether the Pythagorean Theorem applies to the triangle formed by points E, D, and F, we first need to analyze the angles and sides provided.

You have:

  • Angle E = 60°
  • Angle D = 30°
  • Angle F is unknown
  • Side between F and E = 15
  • Side between F and D = 20

To find angle F, we use the fact that the sum of the angles in a triangle is 180°: \[ \text{Angle F} = 180° - (\text{Angle E} + \text{Angle D}) = 180° - (60° + 30°) = 180° - 90° = 90° \]

Since angle F is 90°, this triangle is a right triangle.

The Pythagorean Theorem applies specifically to right triangles, which 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.

Therefore, the correct answer to the question is:

Yes, because it is a right triangle.