Ramon secured an 8 foot volleyball net pole to the ground with a rope attached to the top of the pole and staked in the ground, 5 feet from the base of the vertical pole. What is the angle formed between the top of the pole and the rope? Round your answer to the nearet degree
To find the angle formed between the top of the pole and the rope, we first need to find the length of the rope using Pythagorean theorem.
The length of the rope is the hypotenuse of a right triangle where the vertical pole is the height and the distance from the base of the pole to the stake is the base.
Let x be the length of the rope:
x^2 = 8^2 + 5^2
x^2 = 64 + 25
x^2 = 89
x = √89
x ≈ 9.43 feet
Now we can find the angle using trigonometry:
sin(angle) = opposite/hypotenuse
sin(angle) = 8/9.43
angle = sin^(-1)(8/9.43)
angle ≈ 59 degrees
Therefore, the angle formed between the top of the pole and the rope is approximately 59 degrees.