To solve this problem, we can use the Pythagorean theorem. We have a triangle formed by the height of the screen, the distance from the base to the anchor point (on the ground), and the length of the bracket.
Given:
- Height of the screen (vertical leg) = 30 ft
- Distance from the base to the anchor point on the ground (horizontal leg) = 6 ft
- Length of the metal bracket (hypotenuse) = 15 ft
We need to find the height at which the bracket should be attached to the screen, which we will call \( h \).
According to the Pythagorean theorem: \[ \text{hypotenuse}^2 = \text{vertical leg}^2 + \text{horizontal leg}^2 \]
Setting up the equation: \[ 15^2 = h^2 + 6^2 \]
Calculating \( 15^2 \) and \( 6^2 \): \[ 225 = h^2 + 36 \]
Now, subtract 36 from both sides: \[ 225 - 36 = h^2 \] \[ 189 = h^2 \]
Now take the square root of both sides to find \( h \): \[ h = \sqrt{189} \]
Calculating \( \sqrt{189} \): \[ h \approx 13.75 \]
Now, since we are asked how far from the ground the brackets should be attached to the frame of the screen, we need to find the attachment point relative to the total height of the screen: \[ \text{attachment point} = 30 - h \] \[ \text{attachment point} \approx 30 - 13.75 = 16.25 \]
However, the question requests the height from the bottom of the screen (0 ft) up to where the bracket is to be attached (upwards). Thus, rounding to the nearest hundredth, the height is:
16.25 ft.
None of the provided options perfectly match this calculated answer; the closest option based on the calculations rendered is: 16.16 ft.
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