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
9.1 m
9.1 m
24.1 cm
24.1 cm
16.8 m
We can use the Pythagorean theorem to find the height of the tent.
The height (h) of the tent is the perpendicular distance from the apex (top) of the pyramid to the base.
Using the Pythagorean theorem, we can write:
h^2 = (slant height)^2 - (base edge/2)^2
Plugging in the given values:
h^2 = 13.5^2 - (20/2)^2
h^2 = 182.25 - 100
h^2 = 82.25
Taking the square root of both sides:
h = √82.25
h ≈ 9.1
Therefore, the height of the tent is approximately 9.1 m.
To find the height of the tent, you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the slant height of the tent forms the hypotenuse of a right triangle, and the height of the tent forms one of the legs.
Using the Pythagorean theorem, you can set up the equation:
height^2 + (1/2 * base)^2 = slant height^2
Plugging in the values given in the problem:
height^2 + (1/2 * 20m)^2 = 13.5m^2
Simplifying the equation:
height^2 + 100m^2/4 = 182.25m^2
height^2 + 25m^2 = 182.25m^2
height^2 = 182.25m^2 - 25m^2
height^2 = 157.25m^2
Taking square root on both sides to find the height:
height = √(157.25m^2)
height ≈ 12.5m
Therefore, the height of the tent is approximately 12.5m.
To find the height of the tent, we can use the Pythagorean theorem. The slant height, height, and half the length of the base form a right triangle.
Let's denote the height of the tent as 'h'. We know the length of the base is 20 m and the slant height is 13.5 m.
Using the Pythagorean theorem, we have:
h^2 + (20/2)^2 = 13.5^2
h^2 + 10^2 = 182.25
h^2 + 100 = 182.25
h^2 = 182.25 - 100
h^2 = 82.25
Taking the square root of both sides, we find:
h = √82.25
h ≈ 9.1 m
Therefore, the height of the tent is approximately 9.1 m.