Question

a convenience store owner plans to mount a security camera on the wall behind the cash register. the camera must be mounted (as shown in the figure) to display a good view of the cashier. how high on the wall should the camera be mounted? round your answer to the nearest hundredth. enter your answer in the box.

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle, with adjacent side to the 58° angle being the height \(h\) (what we need to find), and opposite side being 8.5 ft. Use tangent:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Rearrange to solve for height

Rearrange the formula to isolate \(h\):
$h = \frac{8.5}{\tan(58^\circ)}$

Step3: Calculate the value

Use a calculator for $\tan(58^\circ) \approx 1.6003$:
$h \approx \frac{8.5}{1.6003} \approx 5.31$

Answer:

5.31 ft