A bird (B) is spotted flying 900 feet from an observer. The observer (O) also spots the top of a tower (T) at a height of 200 feet. What is the angle of depression from the bird (B) to the observer (O)?
These are the choices:
A) 12.52°
B) 12.84°
C) 77.16°
D) 83.69°

- anonymous

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- anonymous

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- anonymous

I don't want to just know the answer, I'd like to learn it. I know the sin, cos, tan functions btw. I just am a bit confused on this question.

- anonymous

You are given the value of 2 sides, and you want to find an angle,
what trigonometric function of that angle relates the 2 sides?

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## More answers

- anonymous

That would be the sin function right?

- anonymous

yep

- anonymous

\[\sin(x)=\frac{OT}{OB}\]

- anonymous

After simplifying the ratio, you can use a calculator

- anonymous

Okay wouldn't it be sin (x) = 200/900?

- anonymous

yep!

- welshfella

yes I am a little too!
Your diagram does not appear to be right From my understanding the tower is 200 ft high - the diagram shows that the distance to the tower is 200 feet.
I guess the 200 ft must be the distance from the observer to the tower

- anonymous

Okay, then I'd divide 200 into 900 right?

- anonymous

Wait.. What're you saying @welshfella

- welshfella

no you divide 900 into 200

- welshfella

was the diagram given in the question?

- anonymous

\[\sin(x)=\frac{200}{900}=\frac{2}{9}\]

- anonymous

Yes the wording is a little off in the question, it seems like the distance to the tower rather than it's height, but there's no need to think about it too much

- anonymous

What do you mean diagram? Sorry, I'm a bit confused on what I should do now haha.. So should I just switch it around and divide 900 into 200? @welshfella @Nishant_Garg

- welshfella

- but you should query it @ScienceAndMath . Math can be difficult enough without having confusing questions...

- anonymous

|dw:1441025224072:dw|

- anonymous

Okay, so 200 is the distance then?

- anonymous

Since T is 200.

- welshfella

- yes that looks like the problem. I was asking whether the picture you gave was part of the original question.

- anonymous

yep, it looks like that is the case

- anonymous

Yes, this is the exact picture for the question:

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- welshfella

Oh OK then you are on right track The picture is correct but the question has an error.

- anonymous

Okay well if T is the distance should I still use the sin function for 200/900?

- welshfella

yes
Nishant's formula is correct

- anonymous

use a calculator to find arcsin of 200/900, make sure to convert it to degrees if it's in radians

- anonymous

Let me explain what I got and maybe you guys could correct it:
sin(x) = 200/900
(divide 200 into 900)
= 0.2222
sin^-1 0.2222
= 12.838
x 180 divide into pi (3.14)
= 735.95
But then I remember you saying that I should divide 900 into 200..

- anonymous

12.838 approximately 12.84, that's perfect you got your answer there

- anonymous

it was already in degrees you didn't need to convert it

- anonymous

Oh right, I forgot haha, the x 180 divided into pi was just another way to convert it instead of the sin^-1.

- anonymous

one way to remember if you're on right track is that sine and cosine will always give proper fractions
so saying something like
\[\sin(x)=\frac{900}{200}\]
is totally absurd!

- anonymous

Oh okay! So everything works out then?

- anonymous

however sine can also give 1 if the angle is 90, for angles smaller than 90 and greater than 0 it will always give a proper fraction

- anonymous

yep you've done the question

- anonymous

Thank you for all your help!

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