A man walk due west for 4 kilometer, he then change direction and walk on a bearing of 194 degree until he is southwest of his starting point. Hw far is he then from his starting point.
You walk on a HEADING. You take a BEARING.
anyway
west is 270 degrees clockwise from north
270 - 194 = 76 degrees walked south of west on second leg
draw triangle
top horizontal, 4 km long
then down 76 below west which is 180 - 76 = 104 degree inside triangle
then that southwest leg from the start on the upper right down 45 degrees tto
intersection with leg 2
now look at triangle, need long side opposite 104 deg angle
little angle on lower left = 180 - 45 - 104 = 31 degrees
law of sines
sin 31 / 4 = sin 104/ x
solve for x (around 8 km :)