To find the height of the square pyramid, we can use the Pythagorean theorem. The slant height of the pyramid (s) is the hypotenuse of a right triangle formed by the height (h), half the length of the base (b/2), and the slant height.
Using the Pythagorean theorem:
s^2 = (b/2)^2 + h^2
We are given that the length of one of the base sides (b) is 23.8 and the slant height (s) is 89.3.
Plugging in the values:
89.3^2 = (23.8/2)^2 + h^2
Simplifying:
h^2 = 89.3^2 - (23.8/2)^2
h^2 = 7950.49 - 141.64
h^2 = 7808.85
Taking the square root of both sides:
h = √7808.85
h ≈ 88.37
Therefore, the height of the square pyramid is approximately 88.37 inches.
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