We can use trigonometry to solve this problem. Let's draw a diagram:
```
spotlight
*
|\
| \
| \ door
| \
| \
| \
| \
| \
| \
| \
|theta \
------------
distance
```
We want to find the angle theta. We know the opposite side (the height of the spotlight above the floor) and the adjacent side (the distance from the spotlight to the door). We can use the tangent function:
```
tan(theta) = opposite/adjacent
tan(theta) = 7.4/9.3
theta = arctan(7.4/9.3)
theta ≈ 39 degrees
```
Therefore, the answer is A) 39 degrees (rounded to the nearest degree).
. 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). A) 39 degrees. B) 51 degrees. C) 53 degrees. D) 37 degrees
1 answer