Hello, zbrownleep7!

A telephone pole is 60 feet tall.

A guy wire 75 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. Code:

*
* |
* θ |
* |
75 * | 60
* |
* |
* |
* - - - - - - - - - - - +

We want angle $\displaystyle \theta$ in the right triangle.

Its adjacent side is 60 and the hypotenuse is 75.

Since $\displaystyle \cos\theta = \frac{adj}{hyp}$, we have: .$\displaystyle \cos\theta \:=\:\frac{60}{75} \:=\:0.8$

The angle whose cosine is 0.8 is: .$\displaystyle \theta \:=\:\cos^{-1}(0.8) \:=\:36.86989765^o$

Therefore: .$\displaystyle \theta \:\approx\:37^o$