Question

a guy wire is secured near the top of a television transmitting tower. the guy wire meets the ground at an angle of 55°. if the height of the tower is 39 m, how long is the guy wire? round to two decimal places as needed.

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the height of the tower (opposite side to the angle) is 39 m, the guy wire is the hypotenuse (\(c\)), and the angle between the guy wire and the ground is \(55^\circ\). We use the sine function: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(55^\circ)=\frac{39}{c}\).

Step2: Solve for \(c\)

Rearrange the formula: \(c = \frac{39}{\sin(55^\circ)}\). Calculate \(\sin(55^\circ)\approx0.8192\). Then, \(c=\frac{39}{0.8192}\approx47.61\).

Answer:

The length of the guy wire is approximately \(\boldsymbol{47.61}\) meters.