anonymous
  • anonymous
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
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anonymous
  • 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
  • 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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anonymous
  • anonymous
That would be the sin function right?
anonymous
  • anonymous
yep
anonymous
  • anonymous
\[\sin(x)=\frac{OT}{OB}\]
anonymous
  • anonymous
After simplifying the ratio, you can use a calculator
anonymous
  • anonymous
Okay wouldn't it be sin (x) = 200/900?
anonymous
  • anonymous
yep!
welshfella
  • 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
  • anonymous
Okay, then I'd divide 200 into 900 right?
anonymous
  • anonymous
Wait.. What're you saying @welshfella
welshfella
  • welshfella
no you divide 900 into 200
welshfella
  • welshfella
was the diagram given in the question?
anonymous
  • anonymous
\[\sin(x)=\frac{200}{900}=\frac{2}{9}\]
anonymous
  • 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
  • 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
  • welshfella
- but you should query it @ScienceAndMath . Math can be difficult enough without having confusing questions...
anonymous
  • anonymous
|dw:1441025224072:dw|
anonymous
  • anonymous
Okay, so 200 is the distance then?
anonymous
  • anonymous
Since T is 200.
welshfella
  • welshfella
- yes that looks like the problem. I was asking whether the picture you gave was part of the original question.
anonymous
  • anonymous
yep, it looks like that is the case
anonymous
  • anonymous
Yes, this is the exact picture for the question:
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welshfella
  • welshfella
Oh OK then you are on right track The picture is correct but the question has an error.
anonymous
  • anonymous
Okay well if T is the distance should I still use the sin function for 200/900?
welshfella
  • welshfella
yes Nishant's formula is correct
anonymous
  • anonymous
use a calculator to find arcsin of 200/900, make sure to convert it to degrees if it's in radians
anonymous
  • 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
  • anonymous
12.838 approximately 12.84, that's perfect you got your answer there
anonymous
  • anonymous
it was already in degrees you didn't need to convert it
anonymous
  • 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
  • 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
  • anonymous
Oh okay! So everything works out then?
anonymous
  • 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
  • anonymous
yep you've done the question
anonymous
  • anonymous
Thank you for all your help!

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