Given:
B = 30°, a = 4, b = 3
We will solve the triangle to find how many triangles exist that fit the given data
We will use the sine rule to find the angle A as follows:

So, the measure of angle A will be as follows:

Now, we will find the measure of angle C using the fact that the sum of the angles = 180
![\begin{gathered} C=180-(A+B) \\ A=41.81\degree\rightarrow C=180-(30+41.81)=108.19\operatorname{\degree} \\ A=138.19\operatorname{\degree}\rightarrow C=180-(30+138.19)=11.81\operatorname{\degree} \end{gathered}]()
So, there are two triangles that can fit the given data
So, the answer will be Two