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.
16 ft
18 ft
20 ft
14ft
To solve this problem, we can use trigonometry and the concept of a right triangle.
Let's assume that the distance traveled from one end of the conveyor belt to the other is "x" feet.
In the right triangle formed by the ground, the conveyor belt, and the vertical distance (14 feet), the angle between the ground and the conveyor belt is 60°.
Using the trigonometric function sine (sin), we can set up the following equation:
sin(60°) = 14 / x
To solve for x, we can rearrange the equation:
x = 14 / sin(60°)
Using a calculator, we can calculate the value of sin(60°) to be approximately 0.866.
Substituting this back into the equation:
x = 14 / 0.866
Calculating this expression gives us approximately 16.153 feet.
Rounded to the nearest foot, the supplies travel approximately 16 feet from one end of the conveyor belt to the other.
Therefore, the correct answer is 16 ft.