Question

a telephone pole, shown at the top of the next column, is 60 feet tall. a guy wire 89 feet long is attached from the ground to the top of the pole. find the angle between the wire and the pole to the nearest degree. the angle between the wire and the pole is approximately degrees. (round to the nearest degree.)

Explanation:

Step1: Apply cosine function

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, the height of the pole is the adjacent side to the angle $\theta$ between the wire and the pole, and the length of the guy - wire is the hypotenuse. So, $\cos\theta=\frac{60}{89}$.

Step2: Find the angle

We know that $\theta = \cos^{- 1}(\frac{60}{89})$. Calculate $\cos^{-1}(\frac{60}{89})\approx47.2^{\circ}$.

Step3: Round the result

Rounding $47.2^{\circ}$ to the nearest degree gives $47^{\circ}$.

Answer:

$47$