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 nearest foot. (1 point) Responses

21 ft
7 ft
14 ft
17 ft

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the distance the supplies travel from one end of the conveyor belt to the other, we can use trigonometry.

The supplies travel along the hypotenuse of a right triangle, with the angle between the ground and the conveyor belt being 60°. We can use the sine function to find the length of the hypotenuse.

sin(60°) = opposite / hypotenuse
sin(60°) = 12 / hypotenuse

To isolate the hypotenuse, we can rearrange the equation:

hypotenuse = 12 / sin(60°)
hypotenuse ≈ 12 / 0.866 (rounded to three decimal places)

Using a calculator, we find that the hypotenuse is approximately 13.857 feet.

Therefore, the supplies travel approximately 13.857 feet from one end of the conveyor belt to the other. Rounded to the nearest foot, the answer is 14 ft.