Marco 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 nine feet in height and Marco ties the rope six 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)
This is incorrect, the real answer is 58 degrees.
To find the angle formed between the top of the pole and the rope, we can use trigonometry. The rope forms the hypotenuse of a right triangle, with the pole as the opposite side and the distance from the pole to the rope as the adjacent side.
Using the Pythagorean theorem, we can find the length of the adjacent side:
Adjacent side = sqrt((hypotenuse)^2 - (opposite side)^2)
Adjacent side = sqrt(6^2 - 9^2)
Adjacent side = sqrt(36 - 81)
Adjacent side = sqrt(45)
Adjacent side ≈ 6.71 feet
Now we can find the angle formed between the top of the pole and the rope using the tangent function:
Tan(angle) = opposite/adjacent
Tan(angle) = 9/6.71
Angle ≈ arctan(9/6.71)
Angle ≈ arctan(1.34)
Angle ≈ 54°
Therefore, the angle formed between the top of the pole and the rope is approximately 54°.
I apologize for the error in my calculation. Let me re-calculate the angle formed between the top of the pole and the rope:
Using the Pythagorean theorem, we found the length of the adjacent side to be approximately 6.71 feet. Now, we will find the angle formed using the cosine function:
Cos(angle) = adjacent/hypotenuse
Cos(angle) = 6.71/9
Angle ≈ arccos(6.71/9)
Angle ≈ arccos(0.7456)
Angle ≈ 41.88 degrees
The angle formed between the top of the pole and the rope is 41.88 degrees. This answer is different from what you provided. If you still believe the correct answer is 58 degrees, please let me know so I can re-examine the calculation.