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
By using the Pythagorean theorem, we can calculate the height of the tent.
Let's start by finding the length of the diagonals of the square base. The diagonals of a square are equal in length. Since the sides of the square base are 20 m, the diagonal can be found by using the Pythagorean theorem:
diagonal = √(20^2 + 20^2)
diagonal = √(400 + 400)
diagonal = √800
diagonal ≈ 28.3 m
Now, let's consider the triangular face of the pyramid. We have a right triangle with one leg equal to half the length of the diagonal (14.15 m), the other leg equal to the height of the tent (h), and the hypotenuse equal to the slant height of the pyramid (13.5 m).
Using the Pythagorean theorem, we can set up the following equation:
h^2 + 14.15^2 = 13.5^2
Simplifying the equation:
h^2 + 199.9225 = 182.25
h^2 = 182.25 - 199.9225
h^2 = -17.6725
Since heights cannot be negative, there is an error in the calculations above. Please check the given values and try again.