A conveyor belt carries supplies from the first floor to the second floor, which is 14 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
To find the distance the supplies travel, we need to find the hypotenuse of a right triangle. The vertical leg represents the 14 feet increase in height, and the hypotenuse represents the distance traveled by the supplies.
Using trigonometry, we can use the cosine function to find the length of the hypotenuse. The cosine of a 60° angle is equal to the adjacent side (the distance traveled) divided by the hypotenuse.
cos(60°) = adjacent/hypotenuse
cos(60°) = 14/hypotenuse
To find the hypotenuse, we can rearrange the equation:
hypotenuse = 14 / cos(60°)
Using a calculator, we find that the cosine of 60° is approximately 0.5, so:
hypotenuse = 14 / 0.5 = 28
Therefore, the supplies travel a distance of 28 feet from one end of the conveyor belt to the other. Rounded to the nearest foot, the answer is:
Answer: 28 feet
thats not a answer choice
I apologize for the confusion. Let's try to solve the problem using a different approach.
We can treat the conveyor belt as the hypotenuse of a right triangle, with the vertical leg representing the 14 feet increase in height and the horizontal leg representing the distance traveled by the supplies.
To find the distance traveled by the supplies, we can use the sine function, which is opposite/hypotenuse. In this case, the distance traveled is the opposite side.
sin(60°) = 14/hypotenuse
Using a calculator, we find that the sine of 60° is approximately 0.87.
0.87 = 14/hypotenuse
Rearranging the equation:
hypotenuse = 14/0.87 ≈ 16.09
Therefore, the supplies travel a distance of approximately 16.09 feet from one end of the conveyor belt to the other.
Rounded to the nearest foot, the answer is:
Answer: 16 ft