For the square pyramid, the lateral edge E is 25 inches and the slant height S is 24 inches find the height of the pyramid H round to the answer to the nearest home number
In a square pyramid, the slant height (S) is the hypotenuse of a right triangle formed with half the length of a slant edge (E/2) and the height of the pyramid (H) as the other two sides.
Using the Pythagorean theorem, we can solve for H:
H^2 = S^2 - (E/2)^2
H^2 = 24^2 - (25/2)^2
H^2 = 576 - 625/4
H^2 = 2304 - 625/4
H^2 = 2304 - 156.25
H^2 = 2147.75
H ≈ √2147.75
H ≈ 46.34 (rounded to the nearest whole number)
Therefore, the height of the pyramid (H) is approximately 46 inches.