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)
To find the angle of depression, we need to consider the triangle formed by the wall, the floor, and the line of sight from the spotlight to the bottom of the door.
The angle of depression is the angle formed between the line of sight and the horizontal line (floor).
We can use the tangent ratio to find the angle of depression. The opposite side is the height of the spotlight above the floor (7.4 feet), and the adjacent side is the horizontal distance from the spotlight to the door (9.3 feet).
tan(angle) = opposite/adjacent
tan(angle) = 7.4/9.3
angle = arctan(7.4/9.3)
angle ≈ arctan(0.796)
Using a calculator, we find:
angle ≈ 37 degrees
Therefore, the angle of depression from the spotlight to the bottom of the door is approximately 37 degrees.