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.
A. 16.16 ft.
B. 15 ft.
C. 29.39 ft.
D. 13.75 ft.

Answer 1

Use the Pythagorean theorem. If h is the height where the 15-ft bracket meets the screen and the ground anchor is 6 ft from the base, then

h^2 + 6^2 = 15^2
h = sqrt(225 − 36) = sqrt(189) = 3√21 ≈ 13.7477 ≈ 13.75 ft.

Answer: D. 13.75 ft.