Apply the Pythagorean Theorem to determine the height of a building that is a composite of a square prism and a square pyramid on top. The dimensions of the square prism are 40 m by 40 m for the base, and it is 20 m tall. The square pyramid has a slant height of 24 m. Find the height of the building. Round the answer to the nearest tenth.(1 point)
Responses
13.3 m
13.3 m
51.2 m
51.2 m
33.3 m
33.3 m
31.2 m
To find the height of the building, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
First, let's calculate the length of the hypotenuse of the triangle formed by the slant height of the square pyramid and the height of the square prism.
Using the Pythagorean Theorem:
Hypotenuse^2 = base^2 + height^2
24^2 = 40^2 + 20^2
576 = 1600 + 400
576 = 2000
Now, we can solve for the height of the building by subtracting the height of the square prism from the length of the hypotenuse:
Height of the building = Hypotenuse - height of square prism
= √576 - 20
= 24 - 20
= 4
Therefore, the height of the building is 4 meters. Rounded to the nearest tenth, the answer is:
4.0 m