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Sine and Cosine Rule - Bearings

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    Can I get some help on this question.

    A ferry and a cargo ship are both approaching the same port. The ferry is 3.2 km from the port on a bearing of 076° and the cargo ship is 6.9 km from the port on a bearing of 323°.

    Find the distance between the two vessels and the bearing of the cargo ship from the ferry.


    Here is a diagram which I draw from extracting the info from the question to help me answer this

    Is it any correct because it's not helping me, I don't know where to start.

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    The angle between the horizontal and the line connecting the port and the ferry should be 24, for a start. Can you see why?
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    I don't understand, how is that.
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    pretty sure you do this:

    angle at cargo is 37 degrees, use the sine rule to get angle at ferry and then use the fact that angle in a triangle add up to 180 and once you got that, use the cosine rule to to get x
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    (Original post by generalebriety)
    The angle between the horizontal and the line connecting the port and the ferry should be 24, for a start. Can you see why?
    Really?

    (Original post by uer23)
    I don't understand, how is that.
    The angle between the line of 0 degrees and the horizontal line is 90 degrees, you know the bearing is 76 degrees, so 90-76 = 14.
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    This should be your diagram:
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    (Original post by assmaster)
    Really?


    The angle between the line of 0 degrees and the horizontal line is 90 degrees, you know the bearing is 76 degrees, so 90-76 = 14.
    Oh so that means you need a bearing from North to go 76 degrees.
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    (Original post by boromir9111)
    angle at cargo is 37 degrees
    I don't understand how this was deduced ( I can't spot and interior/exterior, alternate or any other type of angles).
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    (Original post by generalebriety)
    The angle between the horizontal and the line connecting the port and the ferry should be 24, for a start. Can you see why?
    is it because 76 + 24 = 90?
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    (Original post by uer23)
    I don't understand how this was deduced ( I can't spot and interior/exterior, alternate or any other type of angles).
    360-323=37
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    Thanks a lot for your help guys I have worked it out finally.
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    (Original post by assmaster)
    Really?
    (Original post by zdo0o)
    is it because 76 + 24 = 90?
    What are you, my primary school? I don't know my times tables either! And I'm proud of it! :mad:

    (Yes, 14. Thank you. :o:)
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    Just need to make sure this is correct as I don't have the answer to this question, can someone check to see if it is right.



    1) Using cosine rule to find Side x

    x^2 = (6.9)^2 + (3.2)^2 - 2(6.9)(3.2) \cos \ (113°)

    x^2 = 75.10468...

    x = \sqrt 75.10468...

    x = 8.67km (3 s.f.)

    2) Using sin rule to find angle Q

    \frac{\sin \ Q}{6.9} = \frac{\sin \ 113°}{8.66629...}

    \sin \ Q = \frac{6.9 \times \sin \ 113°}{8.66629...}

    \sin \ Q = 0.73289...

    Q = \sin^-1(0.73289...)

    Q = 47.12962...°

    3) Bearing of cargo ship from ferry

    Bearing of cargo ship from ferry = P° + Q°

    P° = 360° - 104°

    P° = 256°

    P° + Q° = 256° + 47.12962...°

    = 303.12962...°

    = 303° (3 s.f.)
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    (Original post by generalebriety)
    What are you, my primary school? I don't know my times tables either! And I'm proud of it! :mad:

    (Yes, 14. Thank you. :o:)
    incidentally, i do actually teach year 6 maths at a primary school as part of my gap-year-ing, and i don't know my times tables either
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    Oh you drew the picture wrong, that makes sense now but yeah your method seems right.
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    (Original post by boromir9111)
    Oh you drew the picture wrong, that makes sense now but yeah your method seems right.
    Oh really ? Would you please show me how you would draw the picture.
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    dude look at your first drawing and compare it to the second, quite a big change there and changes how you solve for it (makes it easier now) but that's what i meant, your first drawing was wrong, pay attention and not lash out on me.
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    (Original post by boromir9111)
    dude look at your first drawing and compare it to the second, quite a big change there and changes how you solve for it (makes it easier now) but that's what i meant, your first drawing was wrong, pay attention and not lash out on me.
    :confused: huh? I was not lashing out on you. I thought your comment was referring to my post with the solutions, where you said 'you drew the picture wrong'. So I thought maybe you can show me how it is supposed to be drawn. Be a bit more clear next time.

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Updated: December 9, 2009
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