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.
a. 20 ft
b. 14ft
c. 18 ft
d. 16 ft
We can use trigonometry to find the answer. The side opposite the 60° angle is the vertical distance that the supplies travel (12 feet), and the side adjacent to the 60° angle is the distance that the supplies travel along the conveyor belt. We want to find the hypotenuse, which is the distance from one end of the conveyor belt to the other.
Using the cosine function: cos(60°) = adjacent / hypotenuse
cos(60°) = 12 / hypotenuse
hypotenuse = 12 / cos(60°)
Using a calculator, we find that cos(60°) ≈ 0.5
Therefore, the hypotenuse ≈ 12 / 0.5 ≈ 24 feet.
Rounding to the nearest foot, the supplies travel approximately 24 feet.
Therefore, the correct answer is not listed.