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)
24.1 cm
16.8 m
O91m
14.8 cm
First, we can use the formula for the slant height of a square pyramid to find the height of the triangle. The slant height is the hypotenuse of a right triangle, with the base of the triangle being half the length of one side of the square base of the pyramid (20 m / 2 = 10 m) and the height being the height of the pyramid.
Applying the Pythagorean theorem, we have:
(10 m)^2 + h^2 = (13.5 m)^2
Simplifying:
100 m^2 + h^2 = 182.25 m^2
Subtracting 100 m^2 from both sides:
h^2 = 82.25 m^2
Taking the square root of both sides:
h ≈ 9.1 m
Rounding to the nearest tenth, the height of the tent is approximately 9.1 m.
To find the height of the tent, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the slant height of the tent serves as the hypotenuse, and the height of the tent is one of the other two sides. The side length of the square base is given as 20 m, and the slant height is given as 13.5 m.
Let's calculate the height:
h = √(s^2 - l^2)
where h is the height, s is the side length of the square base, and l is the slant height.
Plugging in the given values, we have:
h = √(20^2 - 13.5^2)
h = √(400 - 182.25)
h = √(217.75)
h ≈ 14.8 m (rounded to the nearest tenth)
Therefore, the height of the tent is approximately 14.8 m.
To find the height of the square pyramid-shaped circus tent, we can use the Pythagorean theorem.
The slant height of the pyramid forms a right triangle with the height and half of the base.
Let's call the height "h" and half of the base "b".
Using the Pythagorean theorem, we have:
b^2 + h^2 = slant height^2
Substituting the given values:
(20/2)^2 + h^2 = (13.5)^2
Simplifying:
10^2 + h^2 = 13.5^2
100 + h^2 = 182.25
h^2 = 182.25 - 100
h^2 = 82.25
Taking the square root of both sides:
h = √82.25
h ≈ 9.08 m
Rounding to the nearest tenth, the height of the circus tent is approximately 9.1 m.
Therefore, the correct answer is: 9.1 m.