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)
• 21 ft
• 7 ft
• 14 f
◎17升
To find the distance the supplies travel from one end of the conveyor belt to the other, we can use the concept of trigonometry.
The 60° angle formed by the conveyor belt with the ground is a right triangle. The opposite side of the triangle represents the vertical distance the supplies travel, which is 12 feet.
We can use the sine function to find the length of the hypotenuse, which represents the total distance the supplies travel.
sin(60°) = opposite/hypotenuse
sin(60°) = 12/hypotenuse
To solve for the hypotenuse, we can rearrange the equation:
hypotenuse = 12/sin(60°)
Using a calculator, we find that sin(60°) ≈ 0.866.
hypotenuse ≈ 12/0.866 ≈ 13.856
Rounding to the nearest foot, the supplies travel approximately 14 feet from one end of the conveyor belt to the other.
Therefore, the answer is 14 ft.