Question

1. 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

Answer 1

Tan α = 9.3 / 7.4 = 1.25675
α = tan ^(-1) 1.25675 = 51.49° ≈ 51°
Answer: B ) the angle of depression from the spotlight to the bottom of the door is 51 degrees.

Answer 2

For this case, we can model the problem as a rectangle triangle.
 We know:
 Height of the triangle.
 Base of the triangle.
 We want to know, angle between the hypotenuse and the base of the triangle.
 For this, we use the following trigonometric relationship:
 $tan \alpha = \frac{7.4}{9.3}$
 Clearing the angle we have:
 $\alpha = arctan(\frac{7.4}{9.3} )$
 $\alpha = 39$
 Answer:
 the angle of depression from the spotlight to the bottom of the door is:
 A) 39 degrees