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
To find the height of the tent, we can use the Pythagorean theorem.
Let h be the height of the tent.
The slant height (l) is the hypotenuse of a right triangle formed by the height, the slant height, and half the length of the square base.
Using the Pythagorean theorem:
20^2 + (0.5 * 20)^2 = 13.5^2
400 + 100 = 182.25
500 = 182.25
500 - 182.25 = h^2
317.75 = h^2
h ≈ 17.8 m
Therefore, the height of the tent is approximately 17.8 meters.
Thats not an answer, the answers are
A: 24.1 CM
B: 16.8 M
C: 9.1 M
D: 14.8 CM
I apologize for my mistake. Let's reevaluate the problem.
We can use the Pythagorean theorem to find the height of the tent.
The height (h) is the side of a right triangle with the slant height as the hypotenuse and half the length of the square base as one of the legs.
Using the Pythagorean theorem:
h^2 + (0.5 * 20)^2 = 13.5^2
h^2 + 10^2 = 182.25
h^2 + 100 = 182.25
h^2 = 182.25 - 100
h^2 = 82.25
h = √82.25
h ≈ 9.1 m
Therefore, the correct answer is C: 9.1 m.