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..