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An illustration shows a triangle with the 90 degree angle symbol located in the lower left. The left-hand side of the triangle extends upward past the vertex. This long line is labeled movie screen and measures 30 feet. The shorter part of the screen that makes up the left-hand side of the triangle is labeled with a question mark. The base is labeled 6 feet and the hypotenuse joining the top of the left vertex and the right vertex of the base is labeled bracket and measures 15 feet.

An outdoor movie screen is 30 ft. tall. It needs additional support to keep it upright and prevent it 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.

29.39 ft.
29.39 ft.

15 ft.
15 ft.

13.75 ft.
13.75 ft.
Remaining Attempts : 3

1 answer

To solve this problem, we can use the Pythagorean theorem, which applies to right triangles. The triangle formed by the screen, the ground, and the line connecting the top of the screen to the anchor point of the bracket can be analyzed here.

We have the following information:

  • The height of the movie screen (vertical side of the triangle) is 30 feet.
  • The distance from the base of the screen to the bracket (horizontal side of the triangle) is 6 feet.
  • The length of the bracket (hypotenuse of the triangle) is 15 feet.

We will denote:

  • \( h \) as the height from the ground to the attachment point of the bracket on the screen.
  • Using the Pythagorean theorem, we know that:

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

Calculating \( 15^2 \) and \( 6^2 \):

\[ 15^2 = 225 \] \[ 6^2 = 36 \]

Substituting into the equation:

\[ h^2 + 36 = 225 \]

Now, subtract 36 from both sides to solve for \( h^2 \):

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

Taking the square root of both sides:

\[ h = \sqrt{189} \approx 13.75 \text{ feet} \]

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

The correct answer is 13.75 ft.