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Math Help - trig word problem, bearings

  1. #1
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    trig word problem, bearings

    This is the problem: A ship is sailing due north. At a certain point the bearing of a lighthouse is N 38 E and the distance is 13.5. After a while, the captain notices that the bearing of the lighthouse is now S 59.4 . How far did the ship travel between the two observations of the lighthouse. distance=?
    Here is what I did: at A the ship tskes a bearing of the lighthouse at C and finds angle A=38 and b=AC=13.5 miles. Later at point B, they find that angle B=59.4. So, angleC= 180-38-59.4=82.6. Next we find c, I used the law of sines, 13.5sin82.6/sin59.4= 15.6 miles.

    I checked and my answer is wrong, so could someone please show me what I did wrong.
    Thank you!
    Keith Stevens
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by kcsteven View Post
    This is the problem: A ship is sailing due north. At a certain point the bearing of a lighthouse is N 38 E and the distance is 13.5. After a while, the captain notices that the bearing of the lighthouse is now S 59.4 . How far did the ship travel between the two observations of the lighthouse. distance=?
    Here is what I did: at A the ship tskes a bearing of the lighthouse at C and finds angle A=38 and b=AC=13.5 miles. Later at point B, they find that angle B=59.4. So, angleC= 180-38-59.4=82.6. Next we find c, I used the law of sines, 13.5sin82.6/sin59.4= 15.6 miles.

    I checked and my answer is wrong, so could someone please show me what I did wrong.
    Thank you!
    Keith Stevens
    Looks OK to me: 15.553511. Checks out on a scale diagram to the limits
    of accuracy of the drawing.

    RonL
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  3. #3
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    Hello, Keith!

    I see absolutely nothing wrong with your work . . .


    A ship is sailing due north. .At a certain point
    the bearing of a lighthouse is N\,38^o\,E and the distance is 13.5 miles.
    After a while, the captain notices that the bearing of the lighthouse is now S\,59.4^o\,E
    How far did the ship travel between the two observations of the lighthouse?

    Here is what I did:
    At A the ship takes a bearing of the lighthouse at C and finds \angle A = 38^o,\;b = AC = 13.5 miles.

    Later at point B, they find that \angle B = 59.4^o.
    So: . \angle C\:= \:180 - 38 - 59.4 \:= \:82.6^o

    Next we find c,
    I used the Law of Sines: . c \:=\:\frac{13.5\sin82.6^o}{\sin59.4^o} \:= \:15.6 miles.

    I checked and my answer is wrong.

    Either: [1] You copied one of the numbers incorrectly
    . . .or: [2] your book is dead wrong.

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