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)
O 8.1 m
O 24.1 cm
O 14.8 cm
O 16.8 m
Let's use the Pythagorean Theorem to find the height of the tent.
The slant height is the hypotenuse of a right triangle, with the two legs being the height and half the length of the square base.
Using the Pythagorean Theorem, we have:
(height)^2 + (10 m)^2 = (13.5 m)^2
(height)^2 + 100 m^2 = 182.25 m^2
(height)^2 = 182.25 m^2 - 100 m^2
(height)^2 = 82.25 m^2
height ≈ √82.25 m^2
height ≈ 9.1 m
Rounded to the nearest tenth, the height of the tent is 9.1 m.
Therefore, the correct answer is:
O 8.1 m
To find the height of the tent, we can use the Pythagorean theorem. The slant height of the pyramid forms the hypotenuse of a right triangle, with one leg being half the length of the square base edge.
Let's call the height of the tent "h" and the leg of the right triangle "x".
Using the Pythagorean theorem, we can say:
x^2 + (10^2) = (13.5^2)
Simplifying the equation:
x^2 + 100 = 182.25
x^2 = 182.25 - 100
x^2 = 82.25
Taking the square root of both sides:
x ≈ √82.25
x ≈ 9.08
Since the height of the tent is double the leg of the right triangle, the height is approximately:
h ≈ 2 * 9.08
h ≈ 18.2
Rounding to the nearest tenth, the height of the tent is approximately 18.2 meters.
Therefore, the correct answer is:
O 16.8 m
To find the height of the tent, you can use the Pythagorean theorem. The slant height of the tent forms the hypotenuse of a right triangle, with each side of the square base forming the other two sides.
Let's label the height of the tent as 'h', and the sides of the square base as 's'. We know that the slant height is 13.5 m, and each side of the square base is 20 m.
Using the Pythagorean theorem, the equation for this right triangle can be written as:
s² + s² = h²
Since each side of the square base is equal (20 m), we can simplify the equation to:
2s² = h²
Now, substituting the given value of the slant height (13.5 m) into the equation, we have:
2(20)² = h²
Simplifying further, we get:
800 = h²
To solve for 'h', we take the square root of both sides of the equation:
h = √800
Using a calculator, we find that the square root of 800 is approximately 28.284.
Therefore, the height of the tent is approximately 28.284 m. Rounding this to the nearest tenth, the answer is 28.3 m.
So, the correct answer is:
- O 28.3 m