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?

Question

GPT 3.5 · Answer

To find the angle formed between the top of the pole and the rope, we can use trigonometry.

Let's denote the angle we're looking for as θ.

From the given information, we have:
- The height of the pole, opposite side from angle θ, is 8 feet
- The distance from the base to where the rope is tied, adjacent side to angle θ, is 5 feet

We can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side:
tan(θ) = opposite/adjacent

Using the values we have:
tan(θ) = 8/5
tan(θ) = 1.6

Now we can find the angle θ by taking the arctan (inverse tangent) of 1.6:
θ = arctan(1.6)

Calculating the arctan(1.6) gives us:
θ ≈ 58.3 degrees

Therefore, the angle formed between the top of the pole and the rope is approximately 58.3 degrees.