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Math Help - sine and consine rules

  1. #1
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    sine and consine rules

    A bird leaves a nest, N, and flies 800 m on a bearing of 132 degrees to a tree T. It then leaves T and flies 650 m on a bearing of 209 degrees to a pylon P. Assuming that N, T and P are at the same height above the ground, calculate the distance and bearing on which the bird must fly in order to return directly from P to N.

    I need your help please ^
    time: 2h+
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  2. #2
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    Start by drawing the situation and marking in all known sides and angles.
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    the calculations are easy?
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  4. #4
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    If you draw the diagram, you will have a triangle with 2 known sides and a known angle in between.

    Law of cosines.
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    Provided you end up with a triangle that has enough known sides/angles in order to solve for the remaining ones, yes.
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    ok, thank you guys
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  7. #7
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    Sine Rule:

    \displaystyle \frac{a}{\sin{A}} = \frac{b}{\sin{B}} = \frac{c}{\sin{C}} or \displaystyle \frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}.


    Cosine Rule:

    \displaystyle c^2 = a^2 + b^2 - 2ab\cos{C} or \displaystyle \cos{C} = \frac{a^2 + b^2 - c^2}{2ab}.
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