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

To apply the Pythagorean theorem to find the height of a square pyramid, we need some context or details about the pyramid, such as the length of the base or the slant height.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is:

\[ c^2 = a^2 + b^2 \]

For a square pyramid, if you're trying to find the vertical height \( h \), you usually start from the apex down to the center of the base, forming a right triangle with half the base length (let's call it \( \frac{s}{2} \), where \( s \) is the length of a side of the base) and the slant height \( l \) (the hypotenuse).

So, the relationship would look like this:

\[ l^2 = h^2 + \left(\frac{s}{2}\right)^2 \]

If you provide the slant height and the length of the base, I can help you determine the height of the pyramid. Please provide those values!

Given that the slant height (\( l \)) is 25 feet and the length of a side of the base (\( s \)) is 40 feet, we can apply the Pythagorean theorem to find the height (\( h \)) of the pyramid.

1. Calculate half the base length: \[ \frac{s}{2} = \frac{40}{2} = 20 \text{ ft} \]

2. Set up the Pythagorean theorem: \[ l^2 = h^2 + \left(\frac{s}{2}\right)^2 \] Substituting the values we have: \[ 25^2 = h^2 + 20^2 \]

3. Calculate the squares: \[ 625 = h^2 + 400 \]

4. Solve for \( h^2 \): \[ h^2 = 625 - 400 = 225 \]

5. Take the square root to find \( h \): \[ h = \sqrt{225} = 15 \text{ ft} \]

Therefore, the height of the square pyramid is 15.0 ft.

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