A straight trail with a uniform inclination of 11° leads from a lodge at an elevation of 700 feet to a mountain lake at an elevation of 5200 feet. What is the length of the trail (to the nearest foot)?

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Answer 1 · 2015-07-20T21:42:48

The length of the trail is #23584# feet to the nearest foot.

The total ascent is #5200# feet #- 700# feet #= 4500# feet.

The length of the trail is the length of the hypotenuse of the right angled triangle with shortest side #4500# feet and opposite angle #11^o#.

So the length of the trail is #(4500 "feet") / (sin 11^o) ~= (4500"feet")/0.190809 ~= 23584# feet

The horizontal distance is #(4500 "feet") / (tan 11^o) ~= 23150# feet