I have a book that covers more advanced trigonometry, unfortunately it does it in a rather terrible way. I have two problems that make me think that I am forgetting some sort of property/rule because I can't solve them quickly. The speed at which I can answer these is crucial.
I realise I have this formatted like it is homework, but it is just because I have two problems that I think use the same principal, hopefully this will help you narrow down what the principal is rather than brute force solving.
Problem 2: Given the following data which can form two triangles
I. Angle C = 30 degrees, c = 8, b = 12 II. Angle B = 45 degrees, a = 12sqrt(2), b = 15sqrt(2) III. Angle C = 60 degrees, b = 12, c = 5sqrt(3)
The answer to that one is only I can make two triangles, II and III can only make one triangle.
From what I can tell both of these can be solved with some concept called an "altitude to base"