Question

A photographer shines a camera light at a particular painting forming an angle of 42 degrees with the camera platform. If the light is 57 feet from the wall where the painting hangs, how high above the platform is the painting?

*triangle drawn in picture attached to the question.*

A. 1.11 ft.
B. 51.32 ft.
C. 63.3 ft.
D. 0.9 ft.

Answer 1

Hello ^_^ Do you know SOHCAHTOA?

Answer 2

??

Answer 3

Trig functions?

Answer 4

Trig functions?

Answer 5

i don't understand?

Answer 6

Jess is referring to the trig identities :

\(\sf \large sin~ \theta = \frac{opposite}{hypotenuse}\\ \large cos~ \theta = \frac{adjacent}{hypotenuse}\\ \large tan~ \theta = \frac{opposite}{adjacent}\)

Answer 7

In your problem, you are given the value of theta= 42° and the adjacent side= 57 ft, and you are looking for the opposite side, so which trig identity should you use to solve for the height(opposite side).

Answer 8

Sorry I'm driving home ill be able to do this math at 3:30pm CA, US time.

Answer 9

@hartnn @Michele_Laino

Answer 10

which sides are involved in this problem?

pick the weird three letter word accordingly and we'll go from there

Answer 11

referring to your drawing in the first reply, we can write:
\[x = 57 \cdot \tan 42\]

Answer 12

you could choose the correct answer using this idea:
45 degrees is special: a 45-45-90 degree triangle has 2 equal sides (in your problem, the distance sideways and the distance up would both be 57 ... *IF* the angle is 45)

but the angle is a bit too small... so we should expect the answer to be *near* 57
but a bit smaller, right ?

Answer 13

Of course, it does not hurt to learn trig, and use SOH CAH TOA to find the exact answer.

Answer 14

thanks for the help everyone. I think the answer is B. 51.32 ft.

Answer 15

That's right! :)