# Math

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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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