Step 1:
\(a)
\The triangle side is and angle is
The laws of sines :
The angle is acute angle,
Recall the relation from the ambiguous case : .
If triangle has one solution and is an acute angle , then
and
and
Substitute ,
in
.
If triangle has one solution, then values of are
and
.
(b)
\If triangle has two solutions and is an acute angle , then
Substitute the corresponding value in above formula
\Divide each side by
Finally conclude that
(c)
\If triangle has no solution and is an acute angle, then
Divide each side by
Substitute and
in above expression.
.
Solution:
\(a)
\ and
(b)
\(c)
\.