Question
A conveyor belt carries supplies from the first floor to the second floor, which is 14 feet higher. The belt makes a 60°%0D%0A60%0D%0A°%0D%0A 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)%0D%0AResponses%0D%0A%0D%0A20 ft%0D%0A20 ft%0D%0A%0D%0A16 ft%0D%0A16 ft%0D%0A%0D%0A18 ft%0D%0A18 ft%0D%0A%0D%0A14 ft
Answers
GPT 3.5
To find the distance that the supplies travel from one end of the conveyor belt to the other, we can use trigonometry.
First, we can find the horizontal component of the distance. This can be found using the cosine function:
cos(60°) = adjacent/hypotenuse
cos(60°) = adjacent/14
adjacent = 14 * cos(60°)
adjacent ≈ 7 feet
Next, we can find the vertical component of the distance. This can be found using the sine function:
sin(60°) = opposite/hypotenuse
sin(60°) = opposite/14
opposite = 14 * sin(60°)
opposite ≈ 12.1 feet
Finally, we can use the Pythagorean theorem to find the total distance:
distance = √(adjacent^2 + opposite^2)
distance = √(7^2 + 12.1^2)
distance ≈ √(49 + 146.41)
distance ≈ √195.41
distance ≈ 13.97 feet
Rounding to the nearest foot, the supplies travel approximately 14 feet from one end of the conveyor belt to the other.
First, we can find the horizontal component of the distance. This can be found using the cosine function:
cos(60°) = adjacent/hypotenuse
cos(60°) = adjacent/14
adjacent = 14 * cos(60°)
adjacent ≈ 7 feet
Next, we can find the vertical component of the distance. This can be found using the sine function:
sin(60°) = opposite/hypotenuse
sin(60°) = opposite/14
opposite = 14 * sin(60°)
opposite ≈ 12.1 feet
Finally, we can use the Pythagorean theorem to find the total distance:
distance = √(adjacent^2 + opposite^2)
distance = √(7^2 + 12.1^2)
distance ≈ √(49 + 146.41)
distance ≈ √195.41
distance ≈ 13.97 feet
Rounding to the nearest foot, the supplies travel approximately 14 feet from one end of the conveyor belt to the other.