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trig

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An electric pole is supported to stand vertically on a level ground by a tight wire. The wire is pegged at a distance of 6 meters from the foot of the pole. The angle that the wire makes the ground is three times the angle it makes with the pole.

  • trig -

    We form a rt. triangle:
    X = 6 meters = Hor.
    Y = Ver. = Dist. from gnd to junction of wire and pole.
    Z = Hyp. = Length of the wire.
    A = Angle bet. gnd and wire.
    B = Angle bet. pole and wire.

    A + B = 90 Deg.
    A = 3B.
    3B + B = 90
    B = 22.5 Deg.
    A = 3B = 3*22.5 = 67.5 Deg.

    Z*cosA = X
    Z = X/cosA = 15.7 m.

    tanA = Y/X = Y/6
    Y = 6*tanA = 6*tan67.5 = 14.5 m.

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