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 tope of the pole and the rope? Round your answer to the nearest whole degree.
We can use the tangent function to solve this problem.
The tangent of an angle can be found by dividing the length opposite the angle by the length adjacent to the angle. In this case, the length opposite the angle is the height of the pole (8 feet) and the length adjacent to the angle is the distance from the base of the pole to the rope (5 feet). So, the tangent of the angle is 8/5.
Let's use a calculator to find the angle whose tangent is 8/5. The inverse tangent (also called arctangent) of 8/5 is approximately 57.99 degrees.
Therefore, the angle formed between the top of the pole and the rope is approximately 58 degrees.