Well-constrained
The smaller inner triangle can be determined since the length of two edges
and the
angle between them is given. The larger inner triangle can now be
determined
since two edge lengths are given and the third can be computed from
the first triangle. Since this new triangle
shares an edge with the first triangle, there
are four possible positions for this triangle with respect to the first
one.
The outer triangle can then be fixed for each of these
configurations because the lengths
of two edges are given, and the angle between the edges can be computed
from the second triangle. Notice that several constraints that are used
to fix the configuration are not given explicitly but instead are
determined implicitly from other constraints.