Question

How many miles long is the slant height of the square pyramid?
one of the lines is 56. one is 33. and one is I

Answer 1

To find the slant height of a square pyramid, we need to determine the relationship between the base, height, and slant height.

In your description, if we assume:
- The base of the pyramid has a length of 56 (which could be the length of a side of the square base).
- The height from the base to the apex is 33.
- The "one is I" is unclear; let’s assume it might represent something else or could be additional context that isn't provided.

The slant height of a pyramid can be calculated using the Pythagorean theorem in a right triangle formed by half of the base, the height, and the slant height.

1. Find half of the length of the base (half of 56):
\[
\text{Half of base} = \frac{56}{2} = 28
\]

2. Use the height (33) and the half base (28) to find the slant height (let's denote it as \( l \)):
\[
l = \sqrt{(\text{height})^2 + (\text{half base})^2} = \sqrt{(33)^2 + (28)^2}
\]
\[
l = \sqrt{1089 + 784} = \sqrt{1873}
\]

3. Calculate \( \sqrt{1873} \):
\[
l \approx 43.30 \text{ miles}
\]

Therefore, the slant height of the square pyramid is approximately 43.30 miles.