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 The Law of Sines:

$$ \dfrac{ a } { \sin( \alpha ) } = \dfrac{ b } { \sin( \beta ) } $$

After substituting $\alpha = 81^o$, $b = 15\, \text{cm}$ and $\beta = 59^o$ we have:

$$ \dfrac{ a } { \sin( 81^o ) } = \dfrac{ 15\, \text{cm} } { \sin( 59^o ) } $$ $$ \dfrac{ a } { 0.9877 } = \dfrac{ 15\, \text{cm} } { 0.8572 } $$ $$ a \cdot 0.8572 = 0.9877 \cdot 15\, \text{cm} $$ $$ a \cdot 0.8572 = 14.8153\, \text{cm} $$ $$ a = \dfrac{ 14.8153\, \text{cm} }{ 0.8572 } $$ $$ a \approx 17.2841\, \text{cm} $$

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