Question

A guy wire supports a cell-phone tower. The guy wire makes a 55° angle with the ground and touches the ground 34 ft from the base of the tower. What is the length of the guy wire, rounded to the nearest foot? 20 ft 28 ft 49 ft 59 ft.

Answer 1

(d) 59 ft

Explanation:

In the geometric model of the problem, the guy wire is the hypotenuse of a right triangle, with the tower being one leg, and the distance along the ground from the tower being the other leg. The ground distance is "adjacent" to the angle of elevation, so the relevant trig function is ...

Cos = Adjacent/Hypotenuse

Solving for the hypotenuse, gives ...

hypotenuse = adjacent/cos(α) = (34 ft)/cos(55°) ≈ 59 ft

The length of the guy wire is about 59 feet.