For the square pyramid, the lateral edge length, e , is 25 in., and the slant height, s , is 24 in. Find the height of the pyramid, h . Round the answer to the nearest whole number. Hint: Before finding the length of h , you will first need to find the length of r
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(1 point)
The height of the square pyramid is ___ in.
To find the height of the square pyramid, we need to find the length of the radius (r) first.
We can use the Pythagorean theorem to find the length of r.
Since the slant height (s) is the hypotenuse of a right triangle with one leg being the height (h) and the other leg being half the length of the base of the pyramid, we can set up the following equation:
s^2 = h^2 + (0.5b)^2
Plugging in the values given in the problem, we get:
24^2 = h^2 + (0.5*25)^2
576 = h^2 + 6.25
h^2 = 576 - 6.25 = 569.75
Taking the square root of both sides, we get:
h = √569.75
Rounding this to the nearest whole number, the height of the square pyramid is approximately:
h ≈ 24