Question

n escalator in the subway station has a vertical rise of 195 ft 9.5 in., and rises at an angle of 10.4°. How long is the escalator? Round to the nearest foot.

Answer 1

To calculate the length of the escalator, convert the vertical rise to feet, use the cosine function with the given angle of incline, and divide the vertical height by the cosine of the angle. The result is approximately 199 feet, which is the length of the escalator when rounded to the nearest foot.

Step-by-step explanation:

To find the length of the escalator, we will use the trigonometric function cosine (cos), because we have the angle of incline and the vertical rise, which is the opposite side of the triangle formed by the escalator's path. The formula to use is cos(θ) = adjacent/hypotenuse, where θ is the angle of incline, the hypotenuse is the escalator length, and the adjacent side is the vertical rise. First, convert the vertical rise to inches and then to feet to ensure consistency in units.

There are 12 inches in a foot, so 195 ft 9.5 in. is equal to 195 × 12 + 9.5 = 2340 + 9.5 = 2349.5 inches. Now convert this to feet by dividing by 12, resulting in 2349.5 / 12 = 195.7917 feet. Next, apply the formula using the angle of 10.4°:

Length of the escalator (hypotenuse) = adjacent side / cos(θ)

Length of the escalator = 195.7917 ft / cos(10.4°)

Using a calculator, find the cos(10.4°) and divide the vertical rise in feet by this number. After performing the calculation, round the answer to the nearest foot.

For example, if cos(10.4°) ≈ 0.982, then the length of the escalator ≈ 195.7917 ft / 0.982 ≈ 199.379 ft, which is rounded to 199 feet.

Answer 2

`l=1085ft`

Step-by-step explanation:

Since the answer is supposed to be feet convert the inches to feet

`195+(9.5)/(12)=195.79ft`

The angle of rise is at the lower floor,so the vertical rise represents the opposite side of a right triangle.The length of the escalator is then hypotenuse of triangle

`Sin(10.4)=(195.79)/(l)\\lSin(10.4)=195.79\\l=(195.79)/(Sin(10.4))\\l=(195.79)/(0.18) \\l=1084.7ft\\round-it\\l=1085ft`