Don't they teach trigonometry at school anymore?? That said, I've forgotten most of it but try the following:
The 'vector triangle' is worked out using the Sine Rule:
Sin A/a = Sin B/b = Sin C/c where a,b and c are the lengths of the triangle (G/S, TAS and Windspeed) and A,B and C are the angles opposing those respective lengths. The problem comes when resolving the angles inside the vector triangle with the bearings given (Wind direction, HDG and TRK). You need to write a suitable algorithim to work these out. Basically if you have any 4 variables you can work out the 2 missing values (Usually HDG and G/S).
You may need to use some other formulae - Cosine rules and/or pythagoras etc., but they all tie in together so a decent GCSE level textbook should provide all you need.
Sorry I can't be of more help but if you can program a computer you damn well ought to have reasonable trig! (I can't program a computer and have v. bad trig)
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