Question

a telephone pole, shown at the top of the next column, is 60 feet tall. a guy wire 76 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: Use cosine function

We know that 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 guy - wire is the hypotenuse. Let the height of the pole $a = 60$ feet and the length of the guy - wire $c=76$ feet. So, $\cos\theta=\frac{60}{76}$.

Step2: Calculate the angle

We have $\theta=\cos^{- 1}(\frac{60}{76})$. First, $\frac{60}{76}\approx0.7895$. Then $\theta=\cos^{-1}(0.7895)$. Using a calculator, $\theta\approx38^{\circ}$.

Answer:

38