Question

A guy-wire is attached to a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the length of the guy wire (round to 2 decimal places)?. . A) 58.15 feet. . B) 143.40 feet. . C) 148.83 feet. . D) 350.62 feet

Answer 1

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:            length of the wire = (137-ft) / (0.390731)

                                                                         =  350.624  .

                      rounded to two decimal places:  350.62 ft