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The interactive applet below shows why the SSA case in the Law of Sines may have 0, 1, or 2 solutions. In this demonstration, we fix side b (segment AC in the picture) and side a (segment BC in the picture), and angle alpha (angle DAC in the picture). The initial picture shows a situation which has no solution. With side b and angle alpha fixed, you can rotate side a around the circle (drag point B with the mouse) and see that no triangle can be created.
Drag point D to create another angle. Drag points C and B to create different lengths for sides a and b. Note that measurements are listed in the upper left corner. If the circle intersects ray AD in two points, then two triangles can be created. If the circle intersects ray AD in just one point, then only one triangle can be created (there are various ways that this can happen). Experiment!