A guy wire runs from the ground to a cell tower.The wire is attached to the cell tower feet above the ground.The angle formed between the wire and the ground is 43° (see figure).How long is the guy wire.

A)166.6 ft
B)146.6 ft
C)156.6 ft
D)161.6 ft
E)151.6 ft

Question

A guy wire runs from the ground to a cell tower.The wire is attached to the cell tower  feet above the ground.The angle formed between the wire and the ground is 43° (see figure).How long is the guy wire. ​
​  ​
A)166.6 ft 
B)​146.6 ft 
C)​156.6 ft 
D)​161.6 ft 
E)​151.6 ft

Quizplus · Accepted Answer

We can use trigonometry to solve this problem. The guy wire, the ground, and the tower form a right triangle. The angle between the ground and the guy wire is 43 degrees, so the angle between the guy wire and the tower is 90 - 43 = 47 degrees.

Let x be the length of the guy wire. Then, using the trigonometric ratios, we have:

sin(43) = opposite/hypotenuse = h/x
cos(43) = adjacent/hypotenuse = 11/x
tan(47) = opposite/adjacent = h/11

Solving for h in the third equation, we get:

h = 11 * tan(47) = 11 * 1.072 = 11.792

Substituting h into the first equation, we get:

sin(43) = 11.792/x

Solving for x, we get:

x = 11.792/sin(43) = 146.6

Therefore, the length of the guy wire is approximately 146.6 feet, which is answer choice B.

A Guy Wire Runs from the Ground to a Cell