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

Answer 1

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

Let's denote:

- \( h \) = height where the brackets are attached to the screen (unknown),
- \( d \) = distance from the base of the screen to where the bracket is anchored = 6 ft,
- \( l \) = length of the bracket = 15 ft.

According to the Pythagorean theorem, we have:

\[
l^2 = h^2 + d^2
\]

Substituting the known values, we have:

\[
15^2 = h^2 + 6^2
\]

Calculating the squares:

\[
225 = h^2 + 36
\]

Now, we subtract 36 from both sides:

\[
225 - 36 = h^2
\]
\[
189 = h^2
\]

Next, we find \( h \) by taking the square root of both sides:

\[
h = \sqrt{189}
\]

Calculating the square root:

\[
h \approx 13.75
\]

Thus, the height from the ground at which the brackets should be attached to the frame of the screen to ensure it is vertical is approximately **13.75 ft**.

Therefore, the correct response is **13.75 ft**.