Question

A security camera in a neighborhood bank is mounted on a wall 12 feetabove the floor. What angle of depression should be used if the camera is tobe directed to a spot 4 feet above the floorand 40 feet from the wall?

Answer 1

Explanation

We are given the following:

• A security camera is mounted on a wall 12 feet above the floor.

We are required to determine the angle of depression when the camera is directed to a spot 4 feet above the floor and 40 feet from the wall.

This can be represented diagrammatically as:

We can extract a triangle from the diagram above as follows:

From the right-angled triangle above, we have:

`\begin{gathered} Opposite=8ft \\ Adjacent=40ft \end{gathered}`

Finally, we can obtain the angle of depression as follows:

`\begin{gathered} \tan\theta=(opposite)/(adjacent) \\ \tan\theta=(8)/(40)=0.2 \\ \tan\theta=0.2 \\ \theta=\tan^(-1)(0.2) \\ \theta\approx11.3\degree \end{gathered}`

Hence, the angle of depression is 11.3°.