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.
By using the Pythagorean theorem, we can calculate the length of the rope.
Let x be the length of the rope:
x^2 = 8^2 + 5^2
x^2 = 64 + 25
x^2 = 89
x = √89
x ≈ 9.4 feet
Now, we can calculate the angle between the top of the pole and the rope using the cosine function:
cos(angle) = 5 / 9.4
angle = arccos(5 / 9.4)
angle ≈ 56°
Therefore, the angle formed between the top of the pole and the rope is approximately 56 degrees.