A 10 ft ten pole has a support rope that extends from the top of the pole to the ground. The rope and the ground form a 30 degree angle. How long is the rope?
To find the length of the rope, we can use the sine function.
In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In this case, the angle is 30 degrees and the side opposite the angle is the length of the rope. The hypotenuse is the length of the pole, which is 10 ft.
The sine of 30 degrees is 0.5. So we can set up the following equation:
0.5 = rope length / 10 ft.
To solve for the rope length, we can multiply both sides of the equation by 10 ft:
rope length = 0.5 * 10 ft.
rope length = 5 ft.
Therefore, the length of the rope is 5 ft.