Thread: trig word problem

i have a question that i hope someone can help me with.

Orienteering is a sport in which competitors use a map and a compass to find their way through unfamiliar terrain. Your task to is to travel along a triangular course. The first leg is due west, and 6,000 meters long. The other two legs are north of the first leg. The second leg is 4,000 m long, and the third leg is 5,000 meters long. Your compass bearing (the direction in which you are moving) during the second leg is degrees _______. During the third leg of your course your bearing is ___ degrees. (answer needs at least three digits past decimal.)

I know that i am supposed to use the law of cosines which is c^2=a^2+b^2-2ab*CosC.
i tried doing 6000^2=5000^2+4000^2-2*5000*4000*cos C
and i got cos C=0.125 which makes C=82.819 degrees. but that was not the answer for either leg. and then i tried subtracting 180 from it but that wasnt the answer either. so i am lost. ( i think that the first bearing should be less than 90 and the second between 90 and 180 but how?)