A straight trail with an inclination of 17 degrees leads a hotel at an of elevation of 9000 feet to a mountain lake at an elevation of 11,200 feet. What is the length of the trail?
I changed your wording just a tad. I hope this is what you mean.
This just sounds like a classic case of right triangle trigonomety. From the hotel, the rise to 11,200 ft. would be 2200 ft. With an inclination of 17 degrees we should have:
$\displaystyle \sin 17=\frac{2200}{x}$
where x is the length of the trail in feet.