Question

The Pythagorean Theorem in Three Dimensions Quick Check

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Question
Use the image to answer the question.

An illustration shows a square pyramid with labeled parts. The left, front and right faces of the pyramid and base are visible. The back face is not visible. The back base edge is not visible but its position is indicated by a dashed line. The front base edge shows a length of 40 feet. A dotted line extends from the interior of the vertex straight down to the center of the base and is labeled h. A right angle is indicated where the dotted height line meets the base. Another dotted line extends from the center of the base where the height line meets to the center of the right base edge. A dotted line extends from the right base edge straight up the center of the right face of the prism and meets the height line at the vertex. This dotted line shows a slant height of 25 feet.

Apply the Pythagorean Theorem to determine the height of the square pyramid, h . Round the answer to the nearest tenth.

(1 point)
Responses

31.2 ft.
31.2 ft.

47.2 ft.
47.2 ft.

15.0 ft.
15.0 ft.

32.0 ft.
32.0 ft.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To apply the Pythagorean Theorem, we can use the right triangle formed by the slant height, the height, and half of the base. Let's call the length of half the base b.

Using the Pythagorean Theorem, we have:

b^2 + h^2 = slant height^2

Since half the base is 40/2 = 20 feet, we have:

20^2 + h^2 = 25^2

400 + h^2 = 625

h^2 = 225

Taking the square root of both sides, we have:

h = 15 feet

So, the height of the square pyramid is 15 feet.

The correct answer is: 15.0 ft.

Answer 2

can you explain