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.
Wrong
Let's assume the distance from the point where the brackets are attached to the ground to the top of the screen is h.
Using the Pythagorean theorem, we can construct a right triangle with the height of the screen (30 ft.), the distance from the base of the screen to the point where the brackets are attached (6 ft.), and the distance from the point where the brackets are attached to the ground (h).
According to the Pythagorean theorem, the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse.
So, we have:
(6 ft.)^2 + h^2 = (30 ft.)^2
36 + h^2 = 900
h^2 = 864
Taking the square root of both sides:
h ≈ ±29.39
We know that h cannot be negative, so h ≈ 29.39 ft.
Therefore, the brackets should be attached to the frame of the screen approximately 29.39 ft. from the ground.