STEP 1: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

After substituting $ \beta = 60^o $ we have:

$$ \alpha + 60^o = 90^o $$ $$ \alpha = 90^o - 60^o $$ $$ \alpha = 30^o $$

STEP 2: find height $ h $

To find height $ h $ use formula:

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

After substituting $\alpha = 30^o$ and $a = 12\, \text{cm}$ we have:

$$ \sin( 30^o ) = \dfrac{ h }{ 12 } $$ $$ \frac{ 1 }{ 2 } = \dfrac{ h }{ 12 } $$$$ h = \frac{ 1 }{ 2 } \cdot 12 $$$$ h = 6 $$

STEP 3: find diagonal $ d2 $

To find diagonal $ d2 $ use formula:

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

After substituting $\beta = 60^o$ and $h = 6\, \text{cm}$ we have:

$$ \sin \left( \frac{ 60^o }{ 2 } \right) = \dfrac{ h }{ d_2 } $$ $$ \sin( 30^o ) = \dfrac{ 6\, \text{cm} }{ d_2 } $$ $$ \frac{ 1 }{ 2 } = \dfrac{ 6\, \text{cm} }{ d_2 } $$ $$ d_2 = \dfrac{ 6\, \text{cm} }{ \frac{ 1 }{ 2 } } $$ $$ d_2 = 12\, \text{cm} $$

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