The sine rule still holds - what you can do is "pivot" the side of length 7 clockwise around the top vertex, maintaining its length, and it will again meet the base and this time theta will be 115 degrees. None of the other stipulated angles/sides are affected. This same ambiguity is why SSA is insufficient to show congruence, because you can have two cases which satisfy the criteria and which are geometrically different shapes.
I thought the first step in solving an SSA triangle (ambiguous case), is to find the altitude from the vertex between the 2 given side lengths to the opposite side - in order to determine if your solution will be 1, 2, or 0 triangles.
There are multiple ways of solving it, or proving that you don't have enough information to solve it. There isn't necessarily a single first step, that is the only possible first step.
I believe sine has two solution because it (y) can be positive twice. in quadrant I and in II. Position 65 in I is 180-65 in II, which is 115. Something like that.
You need at minimum, three pieces of information to define a triangle. 2 angles and a side (AAS / ASA), 2 sides and the angle between them (SAS), all 3 sides (SSS), or knowledge that it is a right triangle and any other two pieces of data. If you have all 6 pieces of information, you've more than fully defined the triangle. The ASS congruence property doesn't exist because of the ambiguous case, where the side opposite the angle has two possible touchdown points. You could get a special case of the ASS triangle, if the opposite side to the given angle touches down at exactly one point. Or you could get no solution.
