STEP 1: find angle $ \alpha $

To find angle $ \alpha $ use formula:

$$ \alpha + \beta + \gamma = 180^o $$

After substituting $\beta = 58^o$ and $\gamma = 62^o$ we have:

$$ \alpha + 58^o + 62^o = 180^o $$ $$ \alpha + 120^o = 180^o $$ $$ \alpha = 180^o - 120^o $$ $$ \alpha = 60^o $$

STEP 2: find side $ a $

To find side $ a $ use The Law of Sines:

$$ \dfrac{ a } { \sin( \alpha ) } = \dfrac{ b } { \sin( \beta ) } $$

After substituting $\alpha = 60^o$, $b = 3\, \text{cm}$ and $\beta = 58^o$ we have:

$$ \dfrac{ a } { \sin( 60^o ) } = \dfrac{ 3\, \text{cm} } { \sin( 58^o ) } $$ $$ \dfrac{ a } { \frac{\sqrt{ 3 }}{ 2 } } = \dfrac{ 3\, \text{cm} } { 0.848 } $$ $$ a \cdot 0.848 = \frac{\sqrt{ 3 }}{ 2 } \cdot 3\, \text{cm} $$ $$ a \cdot 0.848 = \frac{ 3 \sqrt{ 3}}{ 2 }\, \text{cm} $$ $$ a = \dfrac{ \frac{ 3 \sqrt{ 3}}{ 2 }\, \text{cm} }{ 0.848 } $$ $$ a \approx 3.0636\, \text{cm} $$

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