A hiker leaves camp and, using a compass, walks 4 km E, then 6 km S, 3 km E, 5 km...

sounds like one drunk hitch hiker.
well, total north displacement = -6+5+12=11km north
total east displacement=4+3-11=-4=4km west
(11^2+4^2)^0.5=11.7km he has to walk back.
angle from horizontal=Sin^-1(11/11.7)=70.08 degrees or 160.08 from north if ur doing it like that.
 
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