an escalator in the subway system of St. Petersburg, Russia, has a vertical rise of 195 ft 9.5 inch, and rises at an angle of 10.4 degrees. How long is the escalator? Round your answer to the nearest foot.
length=vertical rise/ sin 10.4 deg
To find the length of the escalator, we can use trigonometry.
First, let's convert the height of the escalator from feet and inches to inches:
195 ft × 12 inches/ft = 2340 inches
9.5 inches + 2340 inches = 2349.5 inches
Now, we can use the angle of inclination (10.4 degrees) to find the length of the escalator using the trigonometric function tangent (tan).
The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the escalator (2349.5 inches) and the adjacent side is the length of the escalator.
tan(10.4 degrees) = 2349.5 inches / length of the escalator
To solve for the length of the escalator, we rearrange the equation:
length of the escalator = 2349.5 inches / tan(10.4 degrees)
Using a calculator, we can evaluate the tangent of 10.4 degrees:
tan(10.4 degrees) ≈ 0.1839
Now we can substitute the values and calculate the length of the escalator:
length of the escalator = 2349.5 inches / 0.1839 ≈ 12778.36 inches
Finally, we need to convert the length back to feet:
12778.36 inches ÷ 12 inches/ft ≈ 1064.86 ft
Rounding the answer to the nearest foot, the length of the escalator is approximately 1065 feet.