$\"\"$

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

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The angle $\"\"$ .

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

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Therefore, atleast one solution exists.

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Find the height $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Hence there are two solutions.

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$\"\"$

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$\"\"$

\

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Solution1:

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

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The angle is $\"\"$ .

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Draw the triangle with above specifications:

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$\"\"$

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Law of sines : $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Therefore the $\"\"$ is acute.

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$\"\"$

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

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

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The remaining angle $\"\"$ .

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$\"\"$

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Law of sines : $\"\"$ .

\

$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Solution 2:

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

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Therefore $\"\"$ is obtuse.

\

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

\

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

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The remaining angle $\"\"$ .

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$\"\"$

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Draw the triangle with above specifications.

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$\"\"$

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Law of sines : $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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

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