Find the slant height of the square pyramid. 16 in base and 15 in height.
To find the slant height of a square pyramid, we can use the Pythagorean theorem.
Let's consider one of the triangular faces of the pyramid. We know that the base of the pyramid is a square with side length 16 inches, and the height of the pyramid is 15 inches.
The slant height is the hypotenuse of the right triangle formed by half the base (8 inches), the height (15 inches), and the slant height.
Using the Pythagorean theorem, we have:
slant height^2 = (8 inches)^2 + (15 inches)^2
slant height^2 = 64 inches^2 + 225 inches^2
slant height^2 = 289 inches^2
Taking the square root of both sides:
slant height = √(289 inches^2)
slant height = 17 inches
Therefore, the slant height of the square pyramid is 17 inches.