To find side $ a $ use Law of Cosines:

$$ a^2 = b^2 + c^2 - 2 \cdot b \cdot c \cdot \cos( \alpha ) $$

After substituting $b = 7\, \text{cm}$, $c = 5\, \text{cm}$ and $\alpha = 65^o$ we have:

$$ a^2 = 7^2 + 5^2 - 2 \cdot 7 \cdot 5 \cdot \cos( 65^o ) $$ $$ a^2 = 49\, \text{cm}^2 + 25\, \text{cm}^2 - 2 \cdot 7 \cdot 5 \cdot \cos( 65^o ) $$ $$ a^2 = 74\, \text{cm}^2 - 2 \cdot 35\, \text{cm}^2 \cdot \cos( 65^o ) $$ $$ a^2 = 74\, \text{cm}^2 - 70\, \text{cm}^2 \cdot 0.4226 $$ $$ a^2 = 74\, \text{cm}^2 - 29.5833\, \text{cm}^2 $$ $$ a^2 = 44.4167\, \text{cm}^2 $$ $$ a = \sqrt{ 44.4167\, \text{cm}^2 } $$$$ a \approx 6.6646\, \text{cm} $$

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