Question

An outdoor movie screen is 30 ft. tall. It needs additional support to keep it upright and prevent from leaning. the town has decided to attach 15 ft. metal brackets to the back of the screen. The best spot to anchor the brackets to the ground is 6 ft. from the base of the screen. How far from the ground should the brackets be attached to the frame of the screen to ensure that the screen is at a right angle with the ground? Round to the nearest hundredth.
(1 point)
Responses

16.16 ft.
16.16 ft.
13.75 ft.
13.75 ft.
15 ft.
15 ft.
29.39 ft.

Answer 1

To determine how far from the ground the brackets should be attached to ensure that the screen is at a right angle with the ground, we can use the Pythagorean theorem.

In this scenario, the outdoor movie screen, the ground, and the metal bracket form a right triangle:

- The height of the screen (vertical leg) = 30 ft.
- The distance from the base of the screen to where the bracket is anchored (horizontal leg) = 6 ft.
- The length of the bracket (hypotenuse) = 15 ft.

We can denote:
- \( a = 6 \) ft (the horizontal distance),
- \( b \) = height above ground where the bracket attaches (this is what we want to find),
- \( c = 15 \) ft (the length of the bracket).

According to the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]

Substituting in the values we know:
\[
6^2 + b^2 = 15^2
\]

Calculating each square:
\[
36 + b^2 = 225
\]

Now, isolate \( b^2 \):
\[
b^2 = 225 - 36
\]
\[
b^2 = 189
\]

Taking the square root of both sides to find \( b \):
\[
b = \sqrt{189} \approx 13.75
\]

Thus, the distance from the ground where the brackets should be attached is approximately 13.75 ft.

The correct answer is **13.75 ft.**.