To find side $ a $ use Law of Cosines:
$$ a^2 = b^2 + c^2 - 2 \cdot b \cdot c \cdot \cos( \alpha ) $$After substituting $b = 10$, $c = 12$ and $\alpha = 50^o$ we have:
$$ a^2 = 10^2 + 12^2 - 2 \cdot 10 \cdot 12 \cdot \cos( 50^o ) $$ $$ a^2 = 100 + 144 - 2 \cdot 10 \cdot 12 \cdot \cos( 50^o ) $$ $$ a^2 = 244 - 2 \cdot 120 \cdot \cos( 50^o ) $$ $$ a^2 = 244 - 240 \cdot 0.6428 $$ $$ a^2 = 244 - 154.269 $$ $$ a^2 = 89.731 $$ $$ a = \sqrt{ 89.731 } $$$$ a \approx 9.4726 $$