Aguy-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)?

You need a drawing of the situation to understand, it.
The guy-wire goes from the ground to the pole, its length is x, and has an angle of 67° elevation.
The guy-wire is attached to the ground and a distance of 137 feet from the pole.
Therefore that forms a rectangle triangle. Hypotenuse equals to x, side besides 67° equals to 137. Hence the cosine of that angle equals x divided by 137, that is:
cosine 67 = x/137
solve for x
x = 137 cosine 67
x = 53.5
therefore the guy-wire has a length of 53.5 feet