Question

A circus tent is in the shape of a square pyramid. Each edge of the square base is 20 m and its slant height is 13.5 m. Find the height of the tent. Round the answer to the nearest tenth.(1 point)

Answer 1

To find the height of the tent, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by the height, the slant height, and half the side length of the square base.

Let x be half the side length of the square base.
Using the Pythagorean theorem, we have x^2 + height^2 = slant height^2.
Substituting the given values, we get x^2 + height^2 = 13.5^2.
Since the square base has sides of length 20 m, x = 20/2 = 10 m.
Substituting this value, we get 10^2 + height^2 = 13.5^2.
Simplifying, we get 100 + height^2 = 182.25.
Subtracting 100 from both sides, we get height^2 = 82.25.
Taking the square root of both sides, we get height ≈ 9.1 m.

Therefore, the height of the tent is approximately 9.1 m.