A conveyor belt carries supplies from the first floor to the second floor, which is 14 feet higher. The belt makes a 60°

Question

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)
Responses

20 ft
20 ft

18 ft
18 ft

14 ft
14 ft

16 ft

Answer 1

The distance the supplies travel from one end of the conveyor belt to the other can be calculated using the Pythagorean theorem.

The opposite side of the angle (the vertical distance) is 14 feet. The adjacent side of the angle (the horizontal distance) is the distance the supplies travel.

Using the formula:

hypotenuse^2 = opposite^2 + adjacent^2,

we can solve for the hypotenuse (the distance the supplies travel):

hypotenuse^2 = 14^2 + adjacent^2

Simplifying the equation:

hypotenuse^2 = 196 + adjacent^2

Since the angle is 60°, the hypotenuse is the same as the distance the supplies travel.

We can solve for the adjacent side:

hypotenuse^2 - 196 = adjacent^2

adjacent^2 = hypotenuse^2 - 196

Taking the square root of both sides:

adjacent = √(hypotenuse^2 - 196)

Plugging in the values:

adjacent = √(14^2 - 196)

adjacent = √(196 - 196)

adjacent = 0

Therefore, the adjacent side (the horizontal distance) is 0 feet.

The supplies do not travel horizontally from one end of the conveyor belt to the other. They only travel vertically, a distance of 14 feet.

Therefore, the correct answer is 14 ft.