A fence post is 52.0m from where you are standing, in a direction of 37 degree north of east.A second fence post is due south from you.what is the distance of the second post from you if the distance b/w the two post is 80.0m

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  1. from where you are standing, the angle between the fence posts is
    ... 37º + 90º = 127º

    use the law of sines to find the angle between you and the 1st post
    ... measured from the 2nd post

    sin(Θ) / 52.0 = sin(127º) / 80.0

    the angle (α) between you and the 2nd post, measured from the 1st post is
    ... α = 180º - 127º - Θ

    use the law of sines (again) to find the distance b/w you and the 2nd post

    d / sin(α) = 80.0 / sin(127º)

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  2. using the law of cosines,
    80^2 = x^2 + 52^2 - 104x cos127º
    x = 37

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