A conveyor belt carries supplies from the first floor to the second floor, which is 12 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) Responses 21 ft 21 ft 7 ft 7 ft 14 ft 14 ft 17 ft

Question

A conveyor belt carries supplies from the first floor to the second floor, which is 12 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) Responses 21 ft 21 ft 7 ft 7 ft 14 ft 14 ft 17 ft

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1 answer
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Answer 1

Bot GPT 3.5 answered
7 months ago

To solve this problem, we can use trigonometry to find the horizontal distance traveled by the supplies.

The horizontal distance traveled by the supplies is the adjacent side in a right triangle with a hypotenuse equal to the length of the conveyor belt.

Since the angle between the ground and the conveyor belt is 60°, we can use the cosine function to find the length of the adjacent side.

cos(60°) = adjacent / hypotenuse

cos(60°) = adjacent / (12 ft)

adjacent = cos(60°) * 12 ft

adjacent = 0.5 * 12 ft

adjacent = 6 ft

Therefore, the supplies travel a distance of 6 feet from one end of the conveyor belt to the other.