STEP 1: find angle $ \beta $
To find angle $ \beta $ use formula:
$$ \alpha + \beta + \gamma = 180^o $$After substituting $ \alpha = 81^o $ and $ \gamma = 40^o $ we have:
$$ 81^o + \beta + 40^o = 180^o $$ $$ \beta + 121^o = 180^o $$ $$ \beta = 180^o - 121^o $$ $$ \beta = 59^o $$STEP 2: find side $ a $
To find side $ a $ use Thw Law of Sines:
$$ \dfrac{ a } { \sin( \alpha ) } = \dfrac{ b } { \sin( \beta ) } $$After substituting $\alpha = 81^o$, $b = 15$ and $\beta = 59^o$ we have:
$$ \dfrac{ a } { \sin( 81^o ) } = \dfrac{ 15 } { \sin( 59^o ) } $$ $$ \dfrac{ a } { 0.9877 } = \dfrac{ 15 } { 0.8572 } $$ $$ a \cdot 0.8572 = 0.9877 \cdot 15 $$ $$ a \cdot 0.8572 = 14.8153 $$ $$ a = \dfrac{ 14.8153 }{ 0.8572 } $$ $$ a \approx 17.2841 $$