Specifying two adjacent side lengths 
and 
of a triangle (with 
) and one acute angle 
opposite 
does not, in general, uniquely determine a triangle.
If 
, there are two possible triangles satisfying the given conditions (left figure).
If 
, there is one possible triangle
(middle figure). If 
,
there are no possible triangles (right figure).
Remember: Don't try to prove congruence with the ASS theorem or you will make an ASS out of yourself.
An ASS triangle with sides 
and 
and excluded angle 
with 
has two possible side lengths 
,
 |
The SSS or SAS theorems can then be used with either choice of 
to determine the angles 
and 
and triangle area 
.
