The graph above shows why we can sometimes have no possible triangles sometimes one and sometimes two. Adjust the sliders for , and . You can also drag around point , but it will always be on the circle centered at .
If we are given two sides of a triangle and an angle that is not between them (SSA):

Use the Law of Sines to find sine of the angle

Find both angles in Quadrant I and II with the corresponding reference angle.