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) Responses 14.8 cm 14.8 cm 16.8 m 16.8 m 9.1 m 9.1 m 24.1 cm
To find the height of the tent, we can use the Pythagorean theorem. Let h be the height of the tent.
The slant height forms a right triangle with the height and one side of the square base. The length of the side of the square base is 20m. The hypotenuse is the slant height, which is 13.5m.
Using Pythagorean theorem, we have:
h^2 + 20^2 = 13.5^2
h^2 + 400 = 182.25
h^2 = 182.25 - 400
h^2 = 217.75
h ≈ √217.75
h ≈ 14.8
Therefore, the height of the tent is approximately 14.8m.