Final answer:
The height of the square pyramid is calculated to be approximately 14 inches when rounding to the nearest whole number. This is found by first calculating the half of the base side length (r) and then using the Pythagorean theorem to solve for the height (h).
Step-by-step explanation:
To find the height of the square pyramid, h, we can use the Pythagorean theorem which relates the height (h), the slant height (s), and the half-length of the base (r) of the pyramid. The given lateral edge length is e is 25 in., and the slant height is s is 24 in. First, we need to find the length of r, which is half of the side length of the base of the pyramid. We can form a right triangle with r, h, and s as the sides where the slant height s is the hypotenuse.
Since the pyramid has a square base, the diagonal of the base is e which then relates to r as e = r√2, or, solving for r, r = e / √2. Plugging in the given e = 25 in., we get r = 25 / √2 in. Now we use the Pythagorean theorem to find h: s^2 = h^2 + r^2. Substituting the known values we get 24^2 = h^2 + (25 / √2)^2. Simplifying and solving for h, we get the height of the pyramid. The result should be rounded to the nearest whole number.
Step-by-Step Calculation
Calculate r: r = 25 in / √2 = 17.68 in (approximately)
Apply Pythagorean theorem: 24^2 = h^2 + 17.68^2
Solve for h: h = √(24^2 - 17.68^2) = 14.14 in (approximately)
Round h to the nearest whole number: h = 14 in
The height of the square pyramid is 14 in.