You and a friend decide to set up a volleyball net in your backyard. Each pole that holds the net has a string to secure it to the ground for stability. If the pole is 8 feet tall after being placed in the ground and the stability string is 12 feet long, what is the approximate angle formed between the pole and the string?
42°
42°
48°
48°
73°
73°
90°
To find the angle formed between the pole and the string, we can use trigonometry.
We can consider the string as the hypotenuse of a right triangle, and the pole as the height of the triangle. The stability string forms the diagonal of a right triangle with the pole acting as the vertical side.
Using the Pythagorean theorem, we can find the length of the diagonal:
diagonal^2 = pole^2 + string^2
diagonal^2 = 8^2 + 12^2
diagonal^2 = 64 + 144
diagonal^2 = 208
diagonal ≈ √208
diagonal ≈ 14.42 feet
Now, we can use the sine function to find the angle formed between the pole and the string:
sin(angle) = pole / diagonal
sin(angle) = 8 / 14.42
angle ≈ arcsin(0.5542)
angle ≈ 33.89°
The approximate angle formed between the pole and the string is 33.89°, so none of the given answer choices are correct.