## anonymous one year ago 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°

1. anonymous

2. 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.

3. 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?

4. anonymous

That would be the sin function right?

5. anonymous

yep

6. anonymous

$\sin(x)=\frac{OT}{OB}$

7. anonymous

After simplifying the ratio, you can use a calculator

8. anonymous

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

9. anonymous

yep!

10. 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

11. anonymous

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

12. anonymous

Wait.. What're you saying @welshfella

13. welshfella

no you divide 900 into 200

14. welshfella

was the diagram given in the question?

15. anonymous

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

16. 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

17. 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

18. welshfella

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

19. anonymous

|dw:1441025224072:dw|

20. anonymous

Okay, so 200 is the distance then?

21. anonymous

Since T is 200.

22. welshfella

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

23. anonymous

yep, it looks like that is the case

24. anonymous

Yes, this is the exact picture for the question:

25. welshfella

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

26. anonymous

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

27. welshfella

yes Nishant's formula is correct

28. anonymous

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

29. 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..

30. anonymous

31. anonymous

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

32. anonymous

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

33. 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!

34. anonymous

Oh okay! So everything works out then?

35. 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

36. anonymous

yep you've done the question

37. anonymous

Thank you for all your help!