Final answer:
Using trigonometry, the hypotenuse of the conveyor belt's right triangle is calculated as approximately 28 feet, rounded to the nearest foot. To find the time it takes to reach the second floor at a speed of 75 ft/min, we calculate and round to approximately 0.4 minutes.
Step-by-step explanation:
The question involves using trigonometry to find the length of the hypotenuse of a right triangle when given one angle and the length of the opposite side. Since the conveyor belt makes a 60° angle with the ground and the height difference is 24 feet, you can use the sine function to find the length of the hypotenuse. The sine of an angle in a right triangle is equal to the opposite side divided by the hypotenuse. So, if we let h represent the length of the hypotenuse, we have:
sin(60°) = 24/h
Therefore, h = 24/sin(60°)
The hypotenuse (h) is the actual distance the supplies travel on the conveyor belt.
To calculate the time it takes for the supplies to reach the second floor, use the formula time = distance/speed. Once the length of the hypotenuse is found, divide it by the speed of the conveyor belt, which is 75 ft/min.
The calculations for the hypotenuse and time are as follows:
- Calculate the hypotenuse: h = 24/sin(60°) ≈ 27.7128 feet
- Round to the nearest foot: h ≈ 28 feet
- Calculate the time: time = 28 feet / 75 ft/min = 0.3733 minutes
- Round to the nearest tenth of a minute: time ≈ 0.4 minutes
Therefore, the correct answers are D) 28 feet for the first part of the question and C) 0.4 minutes for the second part.