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Math Help - Law of Sines Word Problem - Ambiguous Case

  1. #1
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    Law of Sines Word Problem - Ambiguous Case

    Here's the word problem:

    A ship is headed due north at a constant 24 miles per hour. Because of the ocean current, the true course of the ship is 15°. If the currents are a constant 22 miles per hour, in what direction are the currents running?

    I know there's supposed to be two answers but I just keep getting to a point where Im not even sure what angle it is that Im looking for. Any help would be great
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  2. #2
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    help for the problem

    Hello Maryanna,
    First of all, sorry about my weak English (My official language is Portuguese).
    In annexe, I show you my point of view about the problem.
    I hope you understand!
    Bye!
    Attached Thumbnails Attached Thumbnails Law of Sines Word Problem - Ambiguous Case-law-sines.jpg  
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  3. #3
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    Thanks so much! I really appreciate your help!
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  4. #4
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    Quote Originally Posted by maryanna91 View Post
    Here's the word problem:

    A ship is headed due north at a constant 24 miles per hour. Because of the ocean current, the true course of the ship is 15°. If the currents are a constant 22 miles per hour, in what direction are the currents running?

    I know there's supposed to be two answers but I just keep getting to a point where Im not even sure what angle it is that Im looking for. Any help would be great

    Lucio Carvalho has shown 1 solution.

    The attached image is rough. It is not to scale.
    It was quickly drawn & scanned.
    This doesn't solve it, but the image shows the other case.

    You have a triangle with two known sides and 1 known angle.
    Use the \text{Sine Law} to get the answer.

     <br />
\dfrac{\sin\theta}{24} \, = \, \dfrac{\sin(15deg)}{22} <br />


     <br />
\sin\theta \, = \, 24 \dfrac{\sin(15deg)}{22} <br />
(get the arcsin of \theta in degrees.)

    The direction of the current:  \theta + 15

    NOTE: Theta can also take the value 180 - \theta which will give the result as depicted by Lucio Carvalho.
    Attached Thumbnails Attached Thumbnails Law of Sines Word Problem - Ambiguous Case-aship0001.jpg  
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