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Math Help - Application of the Sine Rule

  1. #1
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    Application of the Sine Rule

    Hi everyone,

    As I was teaching myself the Sine Rule, I happened upon the following question, which needless to say has stumped my attempts to solve it thus far:

    Here it is:

    From a fire tower, A, a fire is spotted on a bearing of N42 degrees E. From a second tower, B, the fire is on a bearing of N12 degrees W. The two fire towers are 23 kilometres apart and A is N63 degrees W of B.

    I assume that N 42 degrees E means that the fire is 42 degrees away due East. And N 12 degrees West means that it is 348 degrees True. But I am not in any way confident on that.

    Any help solving this problem will be highly appreciated!

    Thanks,

    Nathaniel
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  2. #2
    Senior Member Educated's Avatar
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    Have you tried drawing a diagram to help you visualise it?
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  3. #3
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    Have you drawn a picture? What is the actual question? i.e, what is the angle/distance from X to Y...?
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  4. #4
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    Sure. I'll attach the one I drew now, and show the calculations I have performed to the present.

    Application of the Sine Rule-sin-ab.jpg)

    I do not think it is correct. (And it certainly isn't artistic!)

    Calculations for Tower B:

    a / sin A = b / Sin B

    x / sin 48 = 23 / sin 81

    x = (23 / sin 81) x sin 48

    x = 17.30

    x should have yielded 27.46


    (Above is my latest variation. I've tried others, but to no avail).


    Thanks,

    Nathaniel
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  5. #5
    Senior Member Educated's Avatar
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    This is very confusing. Bearings always start at north and go clockwise... but in this question, they put make the bearing go counterclockwise.

    Here's my interpretation of it:


    Application of the Sine Rule-bearing-1.png

    Now I don't know where to place the third angle, the third piece of information states: "A is N63 degrees W of B"

    But A isn't west of B, it is to the east of B.

    I'm not getting your picture either BinaryBoy. I thought that the fires were more north than the tower?
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