Stuck on a, but just had an idea thanks to Mango. I think it'll involve splitting up the polygon into triangles.
That was what I was getting at I realise my expression actually took x to be the radius I think so uh ignore that Everything falls into place after that.
Well, I suppose it depends on how 'regular' your shape is. For polygons I suppose it's pretty good since you can pack it tightly into a circle
sin(B+C)=0.5 This means B+C=either 30 or 150 Which means either A=150 or A=30 If A=150, B+C=30 which means sinB<0.5 (since both B and C must be less than 30)
3sinB + 4cosC = 6 If sinB<0.5 then 4cosC must be greater than 4.5, which is impossible obviously hence angle CAB must be 30. That's the best reasoning I could think of.