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March 24, 2017

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A 100 foot vertical tower is to be erected on a side of a hill that makes a 6 degree angle with the horizontal. Find the length of each of the two guy wires that will be anchored 75 feet uphill and downhill from the base of the tower.

  • Math - ,

    I interpret "uphill" and "downhill" as measured on the slope.

    Let the tower be AB, A is the base, C is the point 75' uphill, and D is the point 75' downhill.

    Consider triangle ABC where AC makes θ=6° above the horizontal.
    Therefore angle CAB = 90-θ
    AC=75,
    AB=100,
    CAB=φ90-θ=84°
    By the cosine rule,
    BC²=BA²+AC²-2*AB*BC*cos(φ)
    =100²+75²-2*100*75*cos(84°)
    I get BC=118.56'

    You can find BD in a similar way.

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