Question

An escalator at a shopping center is 200ft and 9in long, and rises at an angle of 15 degrees. What is the vertical rise of the escalator. Round to the nearest inch

Answer 1

Answer: 623 inches

Explanation:

We can model this escalator as a right triangle, in which its length is the hypotenuse and its vertical rise (
`x`) is on of the sides of the triangle (as shown in the figure).

So, if we want to find
`x` we have to use the trigonometric function sine:

`sin(15\°)=(opposite-side)/(hypotenuse)` (1)

Here, the opposite side is
`x` and the hypotenuse is
`200 ft 9 in`.

Now we have to transform
`200 ft 9 in` to inches, in this case we only have to convert
`200 ft` to inches, knowing that
`1 ft=12 in`:

`200 ft (12 in)/(1 ft)=2400 in`

`200 ft + 9 in=2400 in+ 9 in=2409 in`

Substituting this value in (1):

`sin(15\°)=(x)/(2409 in)` (2)

Isolating
`x`:

`x=frac{sin(15\°)}{2409 in}`

Finally:

`x=623.49 in \approx 623 in`