$\"\"$

\

The two lengths are $\"\"$ and $\"\"$ .

\

The angle $\"\"$ .

\

A is acute and $\"\"$ because $\"\"$ .

\

Therefore, atleast one solution exists.

\

Find the height $\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

Hence there are two solutions.

\

$\"\"$

\

$\"\"$

\

\

Solution1:

\

The two lengths are $\"\"$ and $\"\"$ .

\

The angle $\"\"$ .

\

Draw the triangle with above specifications:

\

$\"\"$

\

Law of sines : $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Therefore the $\"\"$ is acute.

\

$\"\"$

\

The sum of the angles in any triangle is $\"\"$ .

\

The two angles are $\"\"$ and $\"\"$ .

\

The remaining angle $\"\"$ .

\

$\"\"$

\

Law of sines : $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

Solution 2:

\

The angle $\"\"$ ,then $\"\"$ .

\

Therefore $\"\"$ is obtuse.

\

The sum of the angles in any triangle is $\"\"$ .

\

The two angles are $\"\"$ and $\"\"$ .

\

The remaining angle $\"\"$ .

\

$\"\"$

\

Draw the triangle with above specifications.

\

$\"\"$

\

Law of sines : $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

In $\"\"$ the remaing measures are $\"\"$ and $\"\"$ and $\"\"$ .

\

In $\"\"$ ,the remaing measures are $\"\"$ and $\"\"$ and $\"\"$ .