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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.

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  1. anonymous
    • one year ago
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    x1= 200/ tan 17°44' = .. x2 = 200/ tan 48°13' = ... The distance it traveled: x₁ - x₂ = ...

  2. FireKat97
    • one year ago
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    |dw:1442888207816:dw| You want to find x

  3. FireKat97
    • one year ago
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    |dw:1442888438629:dw| Start by finding theta and using theta find y

  4. anonymous
    • one year ago
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    how would i find theta?

  5. anonymous
    • one year ago
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    would it be 90 - 48°13'

  6. anonymous
    • one year ago
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    @FireKat97

  7. anonymous
    • one year ago
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    im so lost

  8. anonymous
    • one year ago
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    B = theta + 48°13'

  9. FireKat97
    • one year ago
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    Yup theta is correct sorry I marked beta wrong its |dw:1442888983577:dw|

  10. FireKat97
    • one year ago
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    so, now that you have theta, and you're already given one side, you can find y using trig

  11. anonymous
    • one year ago
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    how? like which theorem?

  12. FireKat97
    • one year ago
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    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
    • one year ago
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    sin

  14. anonymous
    • one year ago
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    y/200

  15. anonymous
    • one year ago
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    jk

  16. anonymous
    • one year ago
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    tan, y/200

  17. FireKat97
    • one year ago
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    yup thats right

  18. FireKat97
    • one year ago
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    so y = ?

  19. anonymous
    • one year ago
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    it is y=0.36397023

  20. anonymous
    • one year ago
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    jk tan(1/200)y)

  21. FireKat97
    • one year ago
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    umm actually by using tan, we get; tanø = y/200 so y = 200.tanø

  22. FireKat97
    • one year ago
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    do you see why?

  23. anonymous
    • one year ago
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    ohh ok yes

  24. FireKat97
    • one year ago
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    yup, and you know what theta is, you had it right before, so sub theta in, to find y.

  25. anonymous
    • one year ago
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    y = 200.tan(90 - 48°13')

  26. FireKat97
    • one year ago
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    yes thats correct! now, we can apply the same techniques, to find z, tell me what you get for z

  27. anonymous
    • one year ago
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    do i use B

  28. FireKat97
    • one year ago
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    yup, use beta

  29. anonymous
    • one year ago
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    B = theta + 48°13'

  30. anonymous
    • one year ago
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    B = (90 - 48°13')+ 48°13'

  31. FireKat97
    • one year ago
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    hang on, use this diagram|dw:1442890296933:dw|

  32. FireKat97
    • one year ago
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    |dw:1442890336639:dw|

  33. FireKat97
    • one year ago
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    hopefully thats clearer

  34. FireKat97
    • one year ago
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    so can you see how you would resolve for beta?

  35. anonymous
    • one year ago
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    not really ;(

  36. anonymous
    • one year ago
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    like what formula should i use

  37. anonymous
    • one year ago
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    beta = 90 - 48°13'

  38. FireKat97
    • one year ago
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    beta = 90 - 17 degrees 44 minutes

  39. FireKat97
    • one year ago
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    do you see why?

  40. FireKat97
    • one year ago
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    My diagrams are really bad hahah sorry about that

  41. anonymous
    • one year ago
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    sorry i took so long to respond!

  42. anonymous
    • one year ago
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    @FireKat97

  43. anonymous
    • one year ago
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    tan(z/200) = beta = tan(z/200)= 90- 17 degrees 44 minutes

  44. anonymous
    • one year ago
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    y=449.20

  45. FireKat97
    • one year ago
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    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?

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