$\"\"$

\

(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.

\

$\"\"$ .

\

$\"\"$

\

(a) $\"\"$ and $\"\"$ .

\

(b) $\"\"$ .

\

(c) $\"\"$ .