## anonymous one year ago A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed the angle of depression to the boat is 17°44'. When the boat stops, the angle of depression is 48°13' . The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

1. anonymous

x1= 200/ tan 17°44' = .. x2 = 200/ tan 48°13' = ... The distance it traveled: x₁ - x₂ = ...

2. FireKat97

|dw:1442888207816:dw| You want to find x

3. FireKat97

|dw:1442888438629:dw| Start by finding theta and using theta find y

4. anonymous

how would i find theta?

5. anonymous

would it be 90 - 48°13'

6. anonymous

@FireKat97

7. anonymous

im so lost

8. anonymous

B = theta + 48°13'

9. FireKat97

Yup theta is correct sorry I marked beta wrong its |dw:1442888983577:dw|

10. FireKat97

so, now that you have theta, and you're already given one side, you can find y using trig

11. anonymous

how? like which theorem?

12. FireKat97

okay, so you have |dw:1442889317113:dw| so you have the "adjacent" side and you're looking for the "opposite", according to S-OH C-AH T-OA which trig function do you think is best to use?

13. anonymous

sin

14. anonymous

y/200

15. anonymous

jk

16. anonymous

tan, y/200

17. FireKat97

yup thats right

18. FireKat97

so y = ?

19. anonymous

it is y=0.36397023

20. anonymous

jk tan(1/200)y)

21. FireKat97

umm actually by using tan, we get; tanø = y/200 so y = 200.tanø

22. FireKat97

do you see why?

23. anonymous

ohh ok yes

24. FireKat97

yup, and you know what theta is, you had it right before, so sub theta in, to find y.

25. anonymous

y = 200.tan(90 - 48°13')

26. FireKat97

yes thats correct! now, we can apply the same techniques, to find z, tell me what you get for z

27. anonymous

do i use B

28. FireKat97

yup, use beta

29. anonymous

B = theta + 48°13'

30. anonymous

B = (90 - 48°13')+ 48°13'

31. FireKat97

hang on, use this diagram|dw:1442890296933:dw|

32. FireKat97

|dw:1442890336639:dw|

33. FireKat97

hopefully thats clearer

34. FireKat97

so can you see how you would resolve for beta?

35. anonymous

not really ;(

36. anonymous

like what formula should i use

37. anonymous

beta = 90 - 48°13'

38. FireKat97

beta = 90 - 17 degrees 44 minutes

39. FireKat97

do you see why?

40. FireKat97

My diagrams are really bad hahah sorry about that

41. anonymous

sorry i took so long to respond!

42. anonymous

@FireKat97

43. anonymous

tan(z/200) = beta = tan(z/200)= 90- 17 degrees 44 minutes

44. anonymous

y=449.20

45. FireKat97

Sorry I was on the train ahaha. I think we should take this slow, so we established that beta is 90 - 17* 44' right? Do you agree?