Finding Tracy's position vector from two displacement legs

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tchouhan
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Homework Statement


The distance traveled by an airplane flying from San Francisco International airport (SFO) to San Jose International (SJC) is 30 nautical miles 36° south of east. Flying from SJC to Tracy, the plane's displacement is 36 nautical miles 52° east of north. What is Tracy's position vector in nautical miles relative to SFO?


Homework Equations



##a^2+b^2=c^2##


The Attempt at a Solution



I've tried to draw a triangle, but the positions are weird. I know I need to use trig, but I can figure out what formula to use, or where to start even. Someone help!
 

Discussion

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What's weird about the positions? Have you checked your sketch with a map of California? After all, Google Maps has covered the globe.
 
SteamKing said:
What's weird about the positions? Have you checked your sketch with a map of California? After all, Google Maps has covered the globe.

Yeah I have, but I don't think I'm getting the angles correctly.

Here's a photo, SF at the top left, SJ south, Tracy east: http://imgur.com/LSEgciu

I'm also not entirely sure what sort of trig to use, only just learned what vectors were yesterday.
 
Well, we can't really provide any suggestions unless we see your work.
 
SteamKing said:
Well, we can't really provide any suggestions unless we see your work.

I went to office hours, and I learned that it was just the Law of Cosines.

such that:

c^2 = (30^2+36^2-2(30*36)cos(ab).