A security camera is set up as shown in the diagram below. Michael, who is 5 feet tall, is standing in its view.
What is x, the horizontal distance in feet of the camera?
Responses
A 29.929.9
B 33.4833.48
C 30.530.5
D 70.770.7
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To find the horizontal distance x of the camera, we can use similar triangles.
The height of Michael is 5 feet, and the height of the camera view is 8 feet. The angle of elevation from Michael's head to the camera lens is 20 degrees.
Using trigonometry: tan(20 degrees) = 5/x
Solving for x: x = 5/tan(20 degrees) ≈ 14.4 feet
Therefore, the horizontal distance x of the camera is approximately 14.4 feet.
None of the provided answer choices align with this calculation, so it may be a good idea to double-check the options or calculations.