To find side $ a $ use The Law of Sines:

$$ \dfrac{ a } { \sin( \alpha ) } = \dfrac{ c } { \sin( \gamma ) } $$

After substituting $\alpha = 81^o$, $c = 7\, \text{cm}$ and $\gamma = 40^o$ we have:

$$ \dfrac{ a } { \sin( 81^o ) } = \dfrac{ 7\, \text{cm} } { \sin( 40^o ) } $$ $$ \dfrac{ a } { 0.9877 } = \dfrac{ 7\, \text{cm} } { 0.6428 } $$ $$ a \cdot 0.6428 = 0.9877 \cdot 7\, \text{cm} $$ $$ a \cdot 0.6428 = 6.9138\, \text{cm} $$ $$ a = \dfrac{ 6.9138\, \text{cm} }{ 0.6428 } $$ $$ a \approx 10.756\, \text{cm} $$

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