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
24.1 cm
24.1 cm
14.8 cm
14.8 cm
16.8 m
16.8 m
9.1 m
To find the height of the tent, we can use the Pythagorean theorem. The slant height is one of the legs, and the height of the tent is the other leg. The base of the tent forms the hypotenuse.
Let's denote the height of the tent as "h". Using the Pythagorean theorem, we have:
h^2 + (20/2)^2 = 13.5^2
h^2 + 10^2 = 182.25
h^2 = 182.25 - 100
h^2 = 82.25
Taking the square root of both sides, we have:
h = √82.25
h ≈ 9.1 m
Therefore, the height of the tent is approximately 9.1 m.