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
24.1 cm
24.1 cm
9.1 m
9.1 m
To find the height of the tent, we can use the Pythagorean theorem. The height of the tent is the hypotenuse of a right triangle with one leg being half the length of the square base and the other leg being the slant height.
The length of half the square base is 20/2 = 10 m.
Using the Pythagorean theorem, we have:
height^2 = (10)^2 + (13.5)^2
height^2 = 100 + 182.25
height^2 = 282.25
height ≈ √282.25 ≈ 16.8 m
Therefore, the height of the tent is approximately 16.8 m.