Question

A security camera is mounted 9 feet above the floor .

Answer 1

Answer:

$angle = 0.24 rad = 14 °$

Step-by-step explanation:

The angle of depression is the angle formed by the horizontal at the camera position and the line formed by the camera and the objective, therefore it can be calculated from the information provided as shown in the attached file:

First, you draw f' and f" as parallel lines to the floor at the height of the objective and the height of the camera respectively. Then draw the line o between camera and objective.

the blue angle created by o and f" is the depression angle, which is the same as the angle created by o and f' because angles between parallel lines.

You need to calculate b, as:

b = h - a = 9 - 6 = 3

Then, for the trigonometric function tangent as we have a rectangle triangle:

$Tan(angle)=\frac{b}{f'}$

therefore:

$angle = Tan^{-1}(\frac{b}{f'} ) = Tan^{-1}(\frac{3}{12} )$

$angle = 0.24 rad = 14 °$