Question

Apply the Pythagorean
Theorem to determine the
height of the square pyramid,
. Round the answer to the
nearest tenth.
(1 point)
h
47.2 ft.
31.2 ft.
32.0 ft.
15.0 ft

Answer 1

To find the height of the square pyramid using the Pythagorean theorem, we need to identify the relationship between the height, the base, and the slant height of the pyramid.

Let's assume:
- \( h \) = height of the pyramid
- \( s \) = slant height
- \( b \) = half the length of the base of the pyramid

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides (the height and half the base).

The formula is:

\[ s^2 = h^2 + b^2 \]

In your question, you didn't provide which values correspond to \( s \), \( b \), or \( h \). However, let's say you know the slant height and the base length (or half the base length), you can plug those values into the Pythagorean theorem to solve for \( h \).

Suppose you have the following:
- Slant height \( s = 47.2 \) ft
- Half the base length \( b = 15.0 \) ft

Then, following the formula:

1. Square the slant height:
\[
s^2 = (47.2)^2 = 2224.84
\]

2. Square half the base length:
\[
b^2 = (15.0)^2 = 225
\]

3. Substitute into the Pythagorean theorem:
\[
2224.84 = h^2 + 225
\]

4. Solve for \( h^2 \):
\[
h^2 = 2224.84 - 225 = 1999.84
\]

5. Take the square root to find \( h \):
\[
h = \sqrt{1999.84} \approx 44.7 \text{ ft}
\]

If different values were meant to be used, please specify which are the slant height and half the base length so we can perform the calculations accordingly.