A spotlight is mounted on a wall 7.4 feet above the floor in an office building. It is used to light a door 9.3 feet from the wall. To the nearest degree, what is the angle of depression from the spotlight to the bottom of the door?
(1 point)
Responses
51°
51 degrees
39°
39 degrees
53°
53 degrees
37°
37°
Explanation:
To find the angle of depression, we need to consider the right triangle formed by the vertical height of the spotlight, the horizontal distance to the door, and the line of sight from the spotlight to the bottom of the door.
We use the trigonometric function tangent: tan(theta) = opposite/adjacent.
Let theta be the angle we want to find, opposite = 7.4 ft, and adjacent = 9.3 ft.
tan(theta) = 7.4/9.3
theta = arctan(7.4/9.3)
theta ≈ 37°
Therefore, the angle of depression from the spotlight to the bottom of the door is approximately 37 degrees.