Aguy wire is attached to the top of a radio antenna and to a point on horizontal ground that is 40.0 meters from the base of the antenna. if the wire makes an angle of 55° with the ground, approximate the length l of the wire. (round your answer to the nearest tenth.)

It is useful to start by drawing a picture to visualize this problem. 

In this case we are going to use the trigonometric function cosine, which is Cos(theta) = adjacent / hypotenuse. 

Cos(55) = 40 / x 

After simplifying we reach the equation: X = 40 /  cos(55)

which would then make the length of the wire 69.7 meters long.