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A 5.0 m tree is leaning 5° from the vertical. To prevent it from leaning any farther, a stake needs to be fastened 2 m from the top of the tree at an angle of 60°with the ground. How far from the base of the tree, to the nearest metre, must the stake be?

  • Math -

    I visualize a triangle ABC such that
    AB = 3
    angle B = 95°
    angle C = 60° , so angle A = 180-95-60 = 25°
    BC = x, our required length

    By the sine law:

    x/sin25 = 3/sin60
    x = 3sin25/sin60 = appr 1.46 m

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