Question

A security camera in a neighborhood bank is mounted on a wall 9 feet above the floor. What angle of depression should be used if the camera is to be directed to a spot 6 feet above the floor and 12 feet from the wall?

Short answer

So, the angle of depression is $14.03°.$

Step-by-step solution

Given Information

Given that a security camera in a neighborhood bank is mounted on a wall 9 feet above the floor. The camera is to be directed to a spot 6 feet above the floor and 12 feet from the wall.

Solution

We have to find the angle of depression.

We can draw a figure of the given problem as: -

We have to find $\angle A.$

Now, in $△ADE,\angle D=90°,AD=12ft,DE=3ft$

So,

$$\begin{gathered} \tan \left(x\right)=\frac{DE}{AD} \\ \tan \left(x\right)=\frac{3}{12} \\ \tan \left(x\right)=\frac{1}{4} \\ x={\tan }^{-1}\left(\frac{1}{4}\right) \\ x=14.03° \end{gathered}$$

So, the angle of depression is $14.03°.$