Question

An escalator at a shopping center is 200 ft 9 in. long, and rises at angle of 15°. What is the vertical rise of the escalator?

Answer 1

`color(white)(xx)2409/4(sqrt6-sqrt2)`

Explanation:

Let vertical rise be `h`.

`color(white)(xx)200Ft=2400Inches`
`color(white)(xx)2400+9=2409` (length of escalator)

`color(white)(xx)h/2409=sin15`

Multiple both sides by 2409:
`color(white)(xx)color(red)(2409*)h/2409=color(red)(2409*)sinpi/12`

`=>h=2409*sin(pi/3-pi/4)`
`color(white)(xxx)=2409*(-sin(pi/4)cos(pi/3)+sin(pi/3)cos(pi/4))`
`color(white)(xxx)=2409*(-1/2sqrt2(1/2)+1/2sqrt3(1/2sqrt2))`
`color(white)(xxx)=2409/4(sqrt6-sqrt2)`