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
9.1 m
9.1 m
16.8 m
To find the height of the tent, we can use the Pythagorean theorem. The slant height, the height, and half the length of one side of the square base form a right triangle.
Let's call the height "h", and half the length of one side of the square base "x".
Using the Pythagorean theorem, we have:
x^2 + h^2 = slant height^2
Substituting the given values, we have:
(x)^2 + h^2 = (13.5)^2
x^2 + h^2 = 182.25
Since each edge of the square base is 20 m, half the length of one side of the square base is 10 m. So, x = 10.
Substituting this value into the equation, we have:
10^2 + h^2 = 182.25
100 + h^2 = 182.25
Subtracting 100 from both sides of the equation, we get:
h^2 = 82.25
Taking the square root of both sides, we find:
h ≈ 9.1 m
Therefore, the height of the tent is approximately 9.1 m.