An SAS triangle can't have two solutions... but this one is strange

<A = 34 degrees. b=24. c=46.

This is an SAS triangle... when I use Law of Cosines, I solved for side a and got a=29.35.

Then I tried using Law of Sines to solve for <B and <C.

If I solve for <B first, I set it up this way:

sin(34)

-------

29.35

=

sin B

--------

24

and I get <B=27.2 degrees. Which means <C=118.8 degrees.

However, if I solve for <C first, I set it up this way:

sin(34)

-------

29.35

=

sin C

--------

46

and I get <C=61.2 degrees. Which means <B=84.8 degrees.

What is going on?! I know I'm missing something here, but I can't figure out what it is!

Please help!