Question

angle of depression - the angle between the horizontal line and the line of sight when looking down at an object. word problems: use both the sine, cosine, and soh cah toa, to help solve the following. 1) two security cameras in a museum must be adjusted to monitor a new display of fossils. the cameras are mounted 6 m above the floor, directly across from each other on opposite walls. the walls are 12 m apart. the fossils are displayed in cases made of wood and glass. the top of the display is 1.5 m above the floor. the distance from the camera on the left to the center of the top of the display is 4.8 m. determine the angle of depression, to the nearest degree for each camera.

Explanation:

Step1: Calculate vertical distance

The cameras are 6 m above the floor and the display is 15 m above the floor. So the vertical distance from the camera to the display is $15 - 6=9$ m.

Step2: Identify horizontal distance

The horizontal distance from the camera to the display is 4.8 m.

Step3: Use tangent function

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the opposite side to the angle of depression is the vertical distance (9 m) and the adjacent side is the horizontal distance (4.8 m). So $\tan\theta=\frac{9}{4.8}= 1.875$.

Step4: Find the angle

To find the angle $\theta$, we take the inverse - tangent of 1.875. $\theta=\tan^{- 1}(1.875)\approx61.93^{\circ}\approx62^{\circ}$.

Answer:

$62^{\circ}$