Solving triangles with trigonometry
Python, 441 chars

from math import*
V=[map(float,raw_input().replace('?','0').split())+[0]]
for i in' '*9:
 W=[]
 for a,b,c,A,B,C,R in V:
  if B and C:A=A or pi-B-C
  if a:
   if A:R=R or a/sin(A)
   else:
    if b and c:A=acos((b*b+c*c-a*a)/2/b/c)
    elif R:N=asin(a/R);W+=[(b,c,a,B,C,N,R)];A=pi-N
  else:a=R*sin(A)
  W+=[(b,c,a,B,C,A,R)]
 V=W
V=[T for T in V if all(t&gt;0 for t in T)]
if V:
 for T in V:print' '.join(map(str,T[:-1]))
else:print'No solution'


Does your typical trig to compute the answer.  The current possible solutions are stored as tuples in V.  Any unknown values are recorded as 0.  A seventh variable R is the value a/sin(A)==b/sin(B)==c/sin(C).

I use a trick where the a/b/c values are cycled each iteration to avoid lots of redundant logic.  The inner loop only needs to compute values of the A side or angle.