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. The slant height of the pyramid (13.5 m) is the hypotenuse of a right triangle formed by the height of the pyramid and half the length of the base.
Let's denote the height of the pyramid as 'h' and half the length of the base as 'a'.
Using the Pythagorean theorem, we have:
h^2 = 13.5^2 - a^2
Since each edge of the square base is 20 m, half the length of the base (a) is 20/2 = 10 m.
Substituting the values, we get:
h^2 = 13.5^2 - 10^2
h^2 = 182.25 - 100
h^2 = 82.25
To find the height, we take the square root of both sides:
h = √82.25
h ≈ 9.1
Therefore, the height of the tent is approximately 9.1 meters.
The slant height of the pyramid forms a right triangle with half of a side of the square base and the height of the pyramid.
Using the Pythagorean theorem, we can find the height.
Let h be the height of the pyramid. Then, we have the equation h^2 + (1/2 * 20)^2 = 13.5^2.
This simplifies to h^2 + 100 = 182.25.
Subtracting 100 from both sides gives us h^2 = 82.25.
Taking the square root of both sides gives us h ≈ 9.1 m.
Therefore, the height of the tent is approximately 9.1 meters. Answer: \boxed{9.1}.
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 length 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 (13.5 m) is the hypotenuse of a right triangle, and we need to find the height of the tent, which is one of the other two sides.
Let's label the sides of the triangle:
- The base of the triangle is one of the edges of the square base of the pyramid, which is 20 m.
- The height of the triangle is the height of the tent, which we need to find.
Using the Pythagorean theorem, we can set up the equation:
(Height)^2 + (Base/2)^2 = (Slant height)^2
Plugging in the given values:
(Height)^2 + (20/2)^2 = 13.5^2
Simplifying:
(Height)^2 + 10^2 = 13.5^2
(Height)^2 + 100 = 182.25
(Height)^2 = 182.25 - 100
(Height)^2 = 82.25
Taking the square root of both sides:
Height ≈ √82.25
Height ≈ 9.1
Therefore, the height of the tent is approximately 9.1 meters.