Firstly, lets talk about your "a,b or c???" issue. The three sides of the triangle are named the Hypotenuse (Hyp), Opposite (Opp) and Adjacent (Adj). The Hyp will always be the LONGEST side of the triangle, the Adj is always the line in between the two angles and the Opp is always the remaining side (you can also remember it as the side opposite the Hyp) this is how I remember then.
Next, when you want to find the angle you use the inverse operation on your calculator by using the two numbers you've been given already and dividing one by the other. For example, if it was to cosine rule you're using you type the on your calculator Cos(to the power of -1) which can be typed by pressing shift on your scientific calculator and then pressing "Cos" Adjacent/Hypotenuse.
Now, the co-sine rule comes into effect when you have the Adjacent and Hypotenuse. You can remember what is what with the acronym SOHCAHTOA and as there are 9 letters every 3 form to make a formula triangle. SOH forms to make Opposite on the top with Sine and Hypotenuse on the bottom, CAH forms to make Adjacent on the top and Co-sine and Hypotenuse on the bottom and finally TOA make Opposite on the top and Tangent and Adjacent on the bottom. The middle letter of the three always goes on top.
Hope this helps and if it doesn't quite, just reply and I'll reply back ASAP.
Good luck for your exam!