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.

Answer 1

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,
BC&sup2=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.