Question

a wire connects the top of a 147 foot tall cell tower to the ground. if the angle between the wire and the tower is 37°, how long is the wire? feet round your answer to the nearest hundredth.

Explanation:

Step1: Set up the cosine relationship

Let the length of the wire be \( l \). The height of the tower (\( 147 \) feet) is adjacent to the \( 37^{\circ} \) angle. Using the cosine formula \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \), we have \( \cos(37^{\circ})=\frac{147}{l} \).

Step2: Solve for \( l \)

Rearrange the formula to \( l = \frac{147}{\cos(37^{\circ})} \). We know that \( \cos(37^{\circ})\approx0.7986 \). Then \( l=\frac{147}{0.7986} \).

Step3: Calculate the value

\( l=\frac{147}{0.7986}\approx184.07 \)

Answer:

\( 184.07 \)