The Pythagorean Theorem in Three Dimensions. Use the image to answer the question. Apply the Pythagorean Theorem to determine the height of the square pyramid, h . Round the answer to the nearest tenth. (1 point)

Question

A. 47.2 ft.
B. 32.0 ft.
C. 15.0 ft.
D. 31.2 ft.

Answer 1

To find the height of the square pyramid using the Pythagorean Theorem, we can create a right triangle using the height, the slant height, and half the length of the base.

In the right triangle, the slant height is 40 ft, half the base length is 24 ft, and the height is h.

Using the Pythagorean Theorem, a^2 + b^2 = c^2, where a and b are the legs of the triangle and c is the hypotenuse (slant height):
(24)^2 + h^2 = (40)^2
576 + h^2 = 1600
h^2 = 1024
h = √1024
h = 32 ft (rounded to the nearest tenth)

Therefore, the height of the square pyramid is 32.0 ft, so the correct answer is option B.