The world's longest escalator is in the subway system of St. Petersburg, Russia. The escalator has a vertical rise of 195 ft. 6 in. and rises at an angle of 10.4°. How long is the escalator?
To find the length of the escalator, we can use the sine function to calculate the length of the hypotenuse of the right triangle formed by the vertical rise and the angle of inclination.
First, we need to convert the vertical rise from feet and inches to just inches. There are 12 inches in a foot, so 195 ft. 6 in. is equal to (195 * 12) + 6 = 2346 inches.
Next, we can use the sine function to find the length of the hypotenuse:
sin(angle) = opposite/hypotenuse
hypotenuse = opposite / sin(angle)
Using a calculator, we can calculate the length of the escalator as follows:
hypotenuse = 2346 / sin(10.4°) ≈ 13455 inches
Therefore, the length of the escalator is approximately 13,455 inches.