To find side $ c $ use Law of Cosines:
$$ c^2 = a^2 + b^2 - 2 \cdot a \cdot b \cdot \cos( \gamma ) $$After substituting $a = 8$, $b = 6$ and $\gamma = 45^o$ we have:
$$ c^2 = 8^2 + 6^2 - 2 \cdot 8 \cdot 6 \cdot \cos( 45^o ) $$ $$ c^2 = 64 + 36 - 2 \cdot 8 \cdot 6 \cdot \cos( 45^o ) $$ $$ c^2 = 100 - 2 \cdot 48 \cdot \cos( 45^o ) $$ $$ c^2 = 100 - 96 \cdot \frac{\sqrt{ 2 }}{ 2 } $$ $$ c^2 = 100 - 48 \sqrt{ 2 } $$ $$ c^2 = 32.1177 $$ $$ c = \sqrt{ 32.1177 } $$$$ c \approx 5.6673 $$