This is the AMBIGUOUS case SSA, (side-side-angle)

Rules about the number of solutions.

1.  If the two given sides are equal in measure, the triangle is isosceles,
and the other two equal angles can easily be found and we have a case of
ASA. 

2. If the given side which is opposite the given angle is greater 
than the other given side, there is one solution.

3.  If the given side which is opposite the given angle is shorter 
than the other given side, then we calculate the product of the longer 
given side times the cosine of the given angle.  If the shorter given 
side is shorter than this number, then the shorter given side is too 
short to form a triangle and there is no solution.  Otherwise there are
two solutions.

Your problem is a=12, b=9, and angle A = 38°.

That's case 2.  The given side which is opposite the given angle A is a=12,
which is greater than the other given side, b=9 so there is one solution.

Edwin