Step 1:

(a)

The triangle side is  and angle is .

The laws of sines : 

The angle is acute angle,

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 .

Step 2:

(b)

Relation from the ambiguous case:  .

If triangle has two solutions and  is an acute angle , then .

Substitute the corresponding value in above formula.

.

Divide each side by .

Consider .

Here .

Thus, .

From (1) and (2), conclude that  .

(c)

Relation from the ambiguous case:  .

If triangle has no solution and  is an acute angle, then .

.

Divide each side by .

Substitute and in above expression.

.

If triangle has no solution and  is an acute angle then .

(a)

 and .

(b)

.

(c)

.