What's the minimum number of information required to solve a triangle? In school, I was always taught that given 3 pieces information with at least the length of one side, it was possible to determine all the measures of a triangle.
However, I recently stumbled on the following problem, to which I found two solutions:

Find all the measures of the triangle that has a $64\unicode{xB0}$ angle opposed to a $48\ cm$ side and adjacent to a $50\ cm$ side.

First solution -> The angles measure $64\unicode{xB0}$, $46.57\unicode{xB0}$ and $69.43\unicode{xB0}$
Second solution -> The angles measure $64\unicode{xB0}$, $5.43\unicode{xB0}$ and $110.57\unicode{xB0}$
So, what's the real minimum number of pieces of information to solve a triangle?

Solution of triangles Wikipedia
The case you have is SSA which is not uniquely specified.
