STEP 1: find angle $ \beta $
To find angle $ \beta $ use formula:
$$ \alpha + \beta + \gamma = 180^o $$After substituting $ \alpha = 20^o $ and $ \gamma = 110^o $ we have:
$$ 20^o + \beta + 110^o = 180^o $$ $$ \beta + 130^o = 180^o $$ $$ \beta = 180^o - 130^o $$ $$ \beta = 50^o $$STEP 2: find side $ a $
To find side $ a $ use Thw Law of Sines:
$$ \dfrac{ a } { \sin( \alpha ) } = \dfrac{ b } { \sin( \beta ) } $$After substituting $\alpha = 20^o$, $b = 6$ and $\beta = 50^o$ we have:
$$ \dfrac{ a } { \sin( 20^o ) } = \dfrac{ 6 } { \sin( 50^o ) } $$ $$ \dfrac{ a } { 0.342 } = \dfrac{ 6 } { 0.766 } $$ $$ a \cdot 0.766 = 0.342 \cdot 6 $$ $$ a \cdot 0.766 = 2.0521 $$ $$ a = \dfrac{ 2.0521 }{ 0.766 } $$ $$ a \approx 2.6789 $$