STEP 1: find angle $ \alpha $
To find angle $ \alpha $ use formula:
$$ \alpha + \beta + \gamma = 180^o $$After substituting $ \beta = 30^o $ and $ \gamma = 106^o $ we have:
$$ \alpha + 30^o + 106^o = 180^o $$ $$ \alpha + 136^o = 180^o $$ $$ \alpha = 180^o - 136^o $$ $$ \alpha = 44^o $$STEP 2: find side $ b $
To find side $ b $ use Thw Law of Sines:
$$ \dfrac{ a } { \sin( \alpha ) } = \dfrac{ b } { \sin( \beta ) } $$After substituting $a = \frac{ 29 }{ 8 }$, $\alpha = 44^o$ and $\beta = 30^o$ we have:
$$ \dfrac{ \frac{ 29 }{ 8 } } { \sin( 44^o ) } = \dfrac{ b } { \sin( 30^o ) } $$ $$ \dfrac{ \frac{ 29 }{ 8 } } { 0.6947 } = \dfrac{ b } { \frac{ 1 }{ 2 } } $$ $$ b \cdot 0.6947 = \frac{ 29 }{ 8 } \cdot \frac{ 1 }{ 2 } $$ $$ b \cdot 0.6947 = \frac{ 29 }{ 16 } $$ $$ b = \dfrac{ \frac{ 29 }{ 16 } }{ 0.6947 } $$ $$ b \approx 2.6092 $$