Solution
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:
[tex]\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{ = }\sqrt{3060} \\ \\ l\text{ = 55.3 meters} \end{gathered}[/tex]Step 3
[tex]\begin{gathered} \theta_1\text{ is the angle the wire made with the horizontal} \\ \\ tan\theta_1\text{ = }\frac{opposite}{adjacent}\text{ = }\frac{36}{42} \\ \\ \theta_1\text{ = tan}^{-1}(\frac{36}{42}) \\ \\ \theta_1\text{ = 40.6} \\ \\ \theta_2\text{ is the angle the wire made with the vertical} \\ \\ tan\theta_2\text{ = }\frac{opposite}{adjacent} \\ \\ tan\theta_2\text{ = }\frac{42}{36} \\ \\ \theta_2\text{ = tan}^{-1}(\frac{42}{36}) \\ \\ \theta_2\text{ = 49.4} \end{gathered}[/tex]Final answer
The length of the wire is 55.3 meters
The angle between the tower and the wire is 49.4
