When trying to find if a triangle has a solution with SSA, I prefer to call the given sides the crane and the hangy down thing. By moving the slider you can change the length of the opposite side. That's the hangy down thing. You can shorten the length to see when there will be no triangle. You can also click on the second triangle to see what it would look like.

Move the slider to figure out when there will be no triangle, 1 triangle, or even two triangles. See if you can write out an algorithm.