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 answer
We can think of the conveyor belt as the hypotenuse of a right triangle, with the vertical distance being 14 feet and the angle between the hypotenuse and the vertical distance being 60°. Using the definition of sine, we have $\sin 60^\circ = \frac{14}{\text{hypotenuse}}$, so the hypotenuse is $\frac{14}{\sin 60^\circ}= \frac{14}{\sqrt{3}/2} = \frac{28}{\sqrt{3}}= \frac{28\cdot \sqrt{3}}{3} \approx\boxed{16\text{ feet}}$.