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March 28, 2017

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A radio tower is supported by a wire fastened to the ground 60 feet away from the base of the tower. If the slope of the wire is 3/2 approximately how long is the wire

  • Algebra - ,

    Using similar triangles and ratios, we can find the height of the tower.
    h/60 = 3/2
    h = 90
    then by Pythagoras:
    let the length of the wire be x
    x^2 = 60^2+90^2
    x = √11700 = appr 108.2 ft

    or

    using trig, let the angle formed by Ø
    tanØ = 3/2
    Ø = 56.31°

    then cosØ = 60/x
    x = 60/cos 56.31° = 108.2

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