Question

The guy wires for an antenna tower areattached 36 meters above the groundlf theother end of the guy wires be attached to theplane, 42 meters from the base of the towerto give appropriate stability, what is thelength (of each wire? What are the anglesbetween the tower and the wires ( and )Youmust show all work on this problem, tool

Answer 1

Step 1:

The figure below illustrate the given informations:

Step 2:

Let the length of the wire be l.

Use the Pythagoras theorem to find the length of the wire:

`\begin{gathered} Opposite^2\text{ + Adjacent}^2\text{ = Hypotenuse}^2 \\ 36^2\text{ + 42}^2\text{ = l}^2 \\ \\ 1296\text{ + 1764 = l}^2 \\ \\ 3060\text{ = l}^2 \\ l\text{ = }√(3060) \\ \\ l\text{ = 55.3 meters} \end{gathered}`

Step 3

`\begin{gathered} \theta_1\text{ is the angle the wire made with the horizontal} \\ \\ tan\theta_1\text{ = }(opposite)/(adjacent)\text{ = }(36)/(42) \\ \\ \theta_1\text{ = tan}^(-1)((36)/(42)) \\ \\ \theta_1\text{ = 40.6} \\ \\ \theta_2\text{ is the angle the wire made with the vertical} \\ \\ tan\theta_2\text{ = }(opposite)/(adjacent) \\ \\ tan\theta_2\text{ = }(42)/(36) \\ \\ \theta_2\text{ = tan}^(-1)((42)/(36)) \\ \\ \theta_2\text{ = 49.4} \end{gathered}`

Final answer

The length of the wire is 55.3 meters

The angle between the tower and the wire is 49.4