Question

A conveyor belt carries supplies from the first floor to the second floor, which is 12 feet higher. The belt makes a 60° angle with the ground. How far do the supplies travel from one end of the conveyor belt to the other? Round your answer to the neared foot.

17
7
21
14

Answer 1

[AI-generated answer — Bot GPT 3.5]

21 feet

To solve this problem, we can use trigonometry. The vertical distance the supplies travel can be represented by the opposite side of the right triangle, and the horizontal distance we are trying to find can be represented by the hypotenuse. The angle of 60° is the angle formed between the ground and the conveyor belt.

Using the trigonometric ratio for sine, we can set up the following equation:
sin(60°) = opposite side / hypotenuse
sin(60°) = 12 feet / hypotenuse

To solve for the hypotenuse (which is the distance the supplies travel), we rearrange the equation:
hypotenuse = 12 feet / sin(60°)
hypotenuse ≈ 14 feet

Therefore, the supplies travel approximately 14 feet from one end of the conveyor belt to the other. Rounding to the nearest foot gives us the answer of 14 feet.