SOLUTION: You bike 35 miles from A to B (due south) and then walk 12 miles from B to C at a bearing of N 35 E.  To go back to A (from C) you catch a ride and your bearing is N 40 W. what i

Algebra ->  Trigonometry-basics -> SOLUTION: You bike 35 miles from A to B (due south) and then walk 12 miles from B to C at a bearing of N 35 E.  To go back to A (from C) you catch a ride and your bearing is N 40 W. what i      Log On


   

Question 1136486: You bike 35 miles from A to B (due south) and then walk 12 miles from B to C at a bearing of N 35 E.  To go back to A (from C) you catch a ride and your bearing is N 40 W. what is the total distance you traveled (bike + walk + ride).
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
as far as i can tell, your angles are not correct.

assuming north 35 degrees east from point B to point C, the angle from point C back to point A needs to be north 15.29393523 degrees west.

only then do the figures check out.

assumin that angle from point C back to point A, i get the distance equal to 26.09429598 miles.

this checks out using right triangles and using the law of sines.

assuming north 40 degrees west from point C to point A doesn't check out.
i get different answers using right triangles from using the law of sines.

after correcting for the angle discrepancy, i get the total distance you traveled as 35 miles going south and 12 miles going north 35 degrees east and 26.09429598 miles going north 15.29393523 degrees west.

that would be a total of 73.09429598 miles.