STEP 1: find angle $ \alpha $
To find angle $ \alpha $ use formula:
$$ \alpha + \beta + \gamma = 180^o $$After substituting $ \beta = 30^o $ and $ \gamma = 120^o $ we have:
$$ \alpha + 30^o + 120^o = 180^o $$ $$ \alpha + 150^o = 180^o $$ $$ \alpha = 180^o - 150^o $$ $$ \alpha = 30^o $$STEP 2: find side $ b $
To find side $ b $ use Thw Law of Sines:
$$ \dfrac{ a } { \sin( \alpha ) } = \dfrac{ b } { \sin( \beta ) } $$After substituting $a = 14$, $\alpha = 30^o$ and $\beta = 30^o$ we have:
$$ \dfrac{ 14 } { \sin( 30^o ) } = \dfrac{ b } { \sin( 30^o ) } $$ $$ \dfrac{ 14 } { \frac{ 1 }{ 2 } } = \dfrac{ b } { \frac{ 1 }{ 2 } } $$ $$ b \cdot \frac{ 1 }{ 2 } = 14 \cdot \frac{ 1 }{ 2 } $$ $$ b \cdot \frac{ 1 }{ 2 } = 7 $$ $$ b = \dfrac{ 7 }{ \frac{ 1 }{ 2 } } $$ $$ b = 14 $$