The pole, the guy wire, and the distance along the ground
all form a right triangle. Please sketch a picture of the set-up
on your scratch paper.
In a right triangle,
      (the side adjacent to one of the acute angles)
divided by
      ( the hypotenuse)
is the cosine of the angle.
In this problem ...
-- the acute angle in the triangle is 67°
-- the distance along the ground is the side adjacent to the angle ... 137-ft.
-- the wire is the hypotenuse of the triangle.
-- so,          cosine(67°) = (137-ft) / (length of the wire)
Multiply each side by
(length of the wire) :    cosine(67°) x (length of the wire) = (137-ft)
Divide each side
by cosine(67°)                  length of the wire = (137-ft) / cosine(67°)
Look up cosine(67°)
on your calculator:Â Â Â Â Â Â length of the wire = (137-ft) / (0.390731)
                                     = 350.624 .
           rounded to two decimal places: 350.62 ft
