A 100foot vertical tower is to be erected on the side of a h

A 100-foot vertical tower is to be erected on the side of a hill that makes a 6° angle with the horizontal (see figure). 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. (Note that x = 100 in the figure. Round your answers to one decimal place.)
ft (shorter wire)
ft (longer wire)

Solution

In this given problem, we can view it as two triangles.

Trianlge 1 :

Angle = 90+6 = 96 degrees

Opposite side length = y

side lengths are 100 and 75 feet respectively.

Let us use cosine law

y^2 = 100^2+75^2-2*100*75*cos96

y = 131.12 ft

Triangle 2 :

Angle = 90-6 = 84 degrees

Opposite side length = y2

side lengths are 100 and 75 feet respectively.

Let us use cosine law

y2^2 = 100^2+75^2-2*100*75*cos84

y2 = 118.56 ft

So longer side is 131.12 feet and shorter side is 118.56 feet.