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.
(1 point)
• 14ft
• 16 ft
• 20 ft
• 18ft
To find the distance the supplies travel from one end of the conveyor belt to the other, we can use the concept of trigonometry.
We have the angle of elevation (θ) of 60° and the vertical distance (14 feet) between the two ends of the conveyor belt.
Using the trigonometric function sine (sin), we can relate the opposite side (14 feet) to the hypotenuse (the distance traveled by the supplies).
Let x be the distance traveled by the supplies.
sin(θ) = opposite/hypotenuse
sin(60°) = 14/x
√3/2 = 14/x
Cross multiplying, we have:
√3 * x = 14 * 2
x = (14 * 2) / √3
Simplifying, we get:
x ≈ 16 feet
Therefore, the supplies travel approximately 16 feet from one end of the conveyor belt to the other.
The correct answer is: 16 ft.