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°

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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°

Mathematics
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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.
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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That would be the sin function right?
yep
\[\sin(x)=\frac{OT}{OB}\]
After simplifying the ratio, you can use a calculator
Okay wouldn't it be sin (x) = 200/900?
yep!
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
Okay, then I'd divide 200 into 900 right?
Wait.. What're you saying @welshfella
no you divide 900 into 200
was the diagram given in the question?
\[\sin(x)=\frac{200}{900}=\frac{2}{9}\]
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
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
- but you should query it @ScienceAndMath . Math can be difficult enough without having confusing questions...
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Okay, so 200 is the distance then?
Since T is 200.
- yes that looks like the problem. I was asking whether the picture you gave was part of the original question.
yep, it looks like that is the case
Yes, this is the exact picture for the question:
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Oh OK then you are on right track The picture is correct but the question has an error.
Okay well if T is the distance should I still use the sin function for 200/900?
yes Nishant's formula is correct
use a calculator to find arcsin of 200/900, make sure to convert it to degrees if it's in radians
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..
12.838 approximately 12.84, that's perfect you got your answer there
it was already in degrees you didn't need to convert it
Oh right, I forgot haha, the x 180 divided into pi was just another way to convert it instead of the sin^-1.
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!
Oh okay! So everything works out then?
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
yep you've done the question
Thank you for all your help!

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