A straight trail with a uniform inclination of 13dgs leads from a lodge at an elevation of 1000 feet to amountain lake at an elevation of 6000 feet what is the length of the trail to the nearest foot?

22227 feet

This is a right triangle with an angle equal to 13 degrees, and the side opposite that angle equal to 5000 ft (6000-1000). We need to find the hypotenuse (which we will call x) of the triangle (i.e., the length of the trail). Because sin(theta)=opposite side/hypotenuse.

Therefore we have:

sin(13 deg)=5000/x

Solving for x:

x=5000/sin(13 deg)=22227

[Be sure that you are using degrees rather than radians; otherwise, you will get a wrong answer. If your calculator is using radians and you don't want to change it, you first need to convert 13 degrees to radians by multiplying 13 by (pi/180).] Using radians, you would do the same as above, but the last line would be:

x=5000/sin(13*pi/180)=22227