STEP 1: find side $ c $
To find side $ c $ use Law of Cosines:
$$ c^2 = a^2 + b^2 - 2 \cdot a \cdot b \cdot \cos( \gamma ) $$After substituting $a = 21$, $b = 18$ and $\gamma = 93^o$ we have:
$$ c^2 = 21^2 + 18^2 - 2 \cdot 21 \cdot 18 \cdot \cos( 93^o ) $$ $$ c^2 = 441 + 324 - 2 \cdot 21 \cdot 18 \cdot \cos( 93^o ) $$ $$ c^2 = 765 - 2 \cdot 378 \cdot \cos( 93^o ) $$ $$ c^2 = 765 - 756 \cdot \left(-0.0523\right) $$ $$ c^2 = 765 - \left(-39.566\right) $$ $$ c^2 = 804.566 $$ $$ c = \sqrt{ 804.566 } $$$$ c \approx 28.3649 $$STEP 2: find angle $ \beta $
To find angle $ \beta $ use Law of Cosines:
$$ b^2 = a^2 + c^2 - 2 \cdot a \cdot c \cdot \cos( \beta ) $$After substituting we have:
$$ 18^2 = 21^2 + 28.3649^2 - 2 \cdot 21 \cdot 28.3649 \cdot \cos( \beta ) $$ $$ 324 = 441 + 804.566 - 1191.3246 \cos( \beta ) $$ $$ 1191.3246 \cos( \beta ) = 441 + 804.566 - 324 $$ $$ 1191.3246 \cos( \beta ) = 921.566 $$ $$ 1191.3246 \cos( \beta ) = 921.566 $$ $$ \cos( \beta ) = 0.7736 $$ $$ \beta = \arccos{ \left( 0.7736 \right)} $$ $$ \beta \approx 39.325^o $$