A security camera is set up as shown in the diagram below. Michael, who is 5 feet tall, is standing in its view.
camera angles
39ft width
25ft hight
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
The horizontal distance x can be calculated using trigonometry. The tangent of the angle θ can be calculated as the ratio of the opposite side (25 ft) to the adjacent side (x ft).
tan(θ) = opp/adj
tan(θ) = 25/x
We also know that tan(18.4 degrees) = 25/x. By rearranging the formula, we can find the value of x:
x = 25 / tan(18.4)
x ≈ 70.7 ft
Therefore, the correct response is D) 70.7.