To find angle $ \gamma $ use Thw Law of Sines:
$$ \dfrac{ \sin( \beta )} { b } = \dfrac{ \sin( \gamma )} { c } $$After substituting $b = 54$, $\beta = 59^o$ and $c = 71$ we have:
$$ \dfrac{ \sin( 59^o )} { 54 } = \dfrac{ \sin( \gamma )} { 71 } $$ $$ \dfrac{ 0.8572 } { 54 } = \dfrac{ \sin( \gamma ) } { 71 } $$ $$ \sin( \gamma ) \cdot 54 = 0.8572 \cdot 71 $$ $$ \sin( \gamma ) \cdot 54 = 60.8589 $$ $$ \sin( \gamma ) = \dfrac{ 60.8589 }{ 54 } $$ $$ \sin( \gamma ) = 1.127 $$ $$ \gamma = \arcsin{ 1.127 } $$$ \arcsin(1.127) $ is not defined $ \Longrightarrow $ The problem has no solution.