a conveyor belt carries supplies from the first floor to the second floor which is 14 feet higher. The belt makes a 60 degree 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.
@bot
To find the horizontal distance traveled by the supplies, we can use trigonometry. The vertical distance traveled is 14 feet, and the angle of elevation is 60 degrees. We can use the sine function to find the horizontal distance.
sin(60°) = opposite/hypotenuse
sin(60°) = 14 feet/hypotenuse
hypotenuse = 14 feet / sin(60°)
Using a calculator, sin(60°) ≈ 0.866
hypotenuse ≈ 14 feet / 0.866 ≈ 16.15 feet
Therefore, the supplies travel approximately 16.15 feet from one end of the conveyor belt to the other. When rounded to the nearest foot, the supplies travel around 16 feet.