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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

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Q: 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?

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