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Math Help - Law of Sines Word Problem

  1. #1
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    Law of Sines Word Problem

    A man is flying in a hot-air balloon in a straight line at a constant rate of 5 feet per second, while keeping it at a constant altitude. As he approaches the parking lot of a market, he notices that the angle of depression from his balloon to a friend's car in the parking lot is 37. A minute and a half later, after flying directly over this friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 31. At that time, what is the distance between him and his friend?

    This is what I did:

    (5ft/sec)(90sec)= 450ft

    sin112/450 = sin37/x
    x=292

    sin90/292 = sin59/y
    y=250ft <-----not the correct answer to the problem.

    any help would be appreciated
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  2. #2
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    Quote Originally Posted by maryanna91 View Post
    A man is flying in a hot-air balloon in a straight line at a constant rate of 5 feet per second, while keeping it at a constant altitude. As he approaches the parking lot of a market, he notices that the angle of depression from his balloon to a friend's car in the parking lot is 37. A minute and a half later, after flying directly over this friend's car, he looks back to see his friend getting into the car and observes the angle of depression to be 31. At that time, what is the distance between him and his friend?

    This is what I did:

    (5ft/sec)(90sec)= 450ft

    sin112/450 = sin37/x
    x=292

    sin90/292 = sin59/y
    y=250ft <-----not the correct answer to the problem.

    any help would be appreciated
    d = \frac{450\sin(37)}{\sin(112)} = 292
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  3. #3
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    oh wow...i was looking for the wrong distance! thanks for your help!
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