Rico secures a volleyball-net pole to the ground with a rope that is attached to the top of the pole and creates a diagonal distance to the ground. The volleyball-net pole creates a 90° angle to the ground. If the pole is eight feet in height and Rico ties the rope five feet from the base of the pole, what is the angle formed between the top of the pole and the rope? Round your answer to the nearest whole degree. (1 point)

Question

GPT-4o mini · Answer

To find the angle formed between the top of the volleyball-net pole and the rope, we can use some basic trigonometry.

First, let's visualize the situation. We have a right triangle where:

The height of the pole (the opposite side) is \(8\) feet.
The distance from the base of the pole to the point where the rope is tied (the adjacent side) is \(5\) feet.

We can use the tangent function, which relates the angle \( \theta \) formed between the top of the pole and the rope:

\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{8}{5} \]

Now, we can find \( \theta \) by taking the arctangent:

\[ \theta = \tan^{-1}\left(\frac{8}{5}\right) \]

Now, let's calculate \( \theta \):

\[ \theta \approx \tan^{-1}(1.6) \]

Using a calculator:

\[ \theta \approx 58.0^\circ \]

Thus, the angle formed between the top of the pole and the rope, rounded to the nearest whole degree, is:

\[ \boxed{58} \]