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)
To find the height of the tent, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by the height, the slant height, and half the side length of the square base.
Let x be half the side length of the square base.
Using the Pythagorean theorem, we have x^2 + height^2 = slant height^2.
Substituting the given values, we get x^2 + height^2 = 13.5^2.
Since the square base has sides of length 20 m, x = 20/2 = 10 m.
Substituting this value, we get 10^2 + height^2 = 13.5^2.
Simplifying, we get 100 + height^2 = 182.25.
Subtracting 100 from both sides, we get height^2 = 82.25.
Taking the square root of both sides, we get height ≈ 9.1 m.
Therefore, the height of the tent is approximately 9.1 m.
To find the height of the tent, we can use the Pythagorean theorem.
The slant height of the pyramid is the hypotenuse of a right triangle formed by the height, half the length of the square base, and the slant height.
Let's call the height of the pyramid "h."
Using the Pythagorean theorem, we have:
h² + (10 m)² = (13.5 m)²
Simplifying the equation, we have:
h² + 100 m² = 182.25 m²
Subtracting 100 m² from both sides of the equation, we have:
h² = 82.25 m²
Taking the square root of both sides of the equation, we have:
h ≈ √82.25
Using a calculator, we find that h ≈ 9.1
Therefore, the height of the tent is approximately 9.1 meters.
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 (in this case, the slant height) is equal to the sum of the squares of the other two sides.
In our scenario, the slant height (hypotenuse) is given as 13.5 m, and the length of one side of the square base is given as 20 m. Let's label the height of the tent as 'h.'
Using the Pythagorean theorem, we can set up the following equation:
h^2 = (20/2)^2 + 13.5^2
Simplifying this equation:
h^2 = 10^2 + 13.5^2
h^2 = 100 + 182.25
h^2 = 282.25
To solve for h, we take the square root of both sides:
h = √282.25
Using a calculator, we find that h ≈ 16.8
Therefore, the height of the tent is approximately 16.8 meters, rounded to the nearest tenth.