Question

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?
39 degrees
51 degrees
53 degrees
37 degrees

Answer 1

I belive you use SOH-CAH-TOA

Answer 2

toa
i got 51 but i wanted to check if its correct

Answer 3

you are right

Answer 4

yay thanks:)))

Answer 5

That's what I got :)

Answer 6

me too

Answer 7

the answer was 39 degrees.... i dont know how but i got it wrong:(

Answer 8

@imqwerty can you explain how i should have done this?

Answer 9

:)

Answer 10

so theta is our angle of depression

we can say that\[\angle(CAB)=\theta \]because theta and angle(CAB) are corresponding angles

now we need to find this theta

\[\tan(CAB)=\frac{ BC }{ AB }\]\[\tan(\theta)=\frac{ 7.4 }{ 9.3 }\]\[\tan(\theta)=0.7956\]\[\theta=\tan^{-1} (0.7956)\]\[\theta=39^{o}\]