STEP 1: find angle $ \alpha $

To find angle $ \alpha $ use formula:

$$ \alpha + \beta = 90^o $$

After substituting $ \beta = 59^o $ we have:

$$ \alpha + 59^o = 90^o $$ $$ \alpha = 90^o - 59^o $$ $$ \alpha = 31^o $$

STEP 2: find height $ h $

To find height $ h $ use formula:

$$ \sin \left( \frac{ \beta }{ 2 } \right) = \dfrac{ h }{ d_2 } $$

After substituting $\beta = 59^o$ and $d_2 = 59\, \text{cm}$ we have:

$$ \sin \left( \frac{ 59^o }{ 2 } \right) = \dfrac{ h }{ d_2 } $$ $$ \sin( \frac{ 59 }{ 2 }^o ) = \dfrac{ h }{ 59 } $$ $$ 0.4924 = \dfrac{ h }{ 59 } $$$$ h = 0.4924 \cdot 59 $$$$ h = 29.053 $$

STEP 3: find side $ a $

To find side $ a $ use formula:

$$ \sin \left( \alpha \right) = \dfrac{ h }{ a } $$

After substituting $\alpha = 31^o$ and $h = 29.053\, \text{cm}$ we have:

$$ \sin( 31^o ) = \dfrac{ 29.053\, \text{cm} }{ a } $$ $$ 0.515 = \dfrac{ 29.053\, \text{cm} }{ a } $$ $$ a = \dfrac{ 29.053\, \text{cm} }{ 0.515 } $$ $$ a = 56.4094\, \text{cm} $$

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