STEP 1: find height $ h $

To find height $ h $ use formula:

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

After substituting $\alpha = 60^o$ and $a = 1\, \text{cm}$ we have:

$$ \sin( 60^o ) = \dfrac{ h }{ 1 } $$ $$ \frac{\sqrt{ 3 }}{ 2 } = \dfrac{ h }{ 1 } $$$$ h = \frac{\sqrt{ 3 }}{ 2 } \cdot 1 $$$$ h = 0.866 $$

STEP 2: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ h }{ d_1 } $$

After substituting $\alpha = 60^o$ and $h = 0.866\, \text{cm}$ we have:

$$ \sin \left( \frac{ 60^o }{ 2 } \right) = \dfrac{ h }{ d_1 } $$ $$ \sin( 30^o ) = \dfrac{ 0.866\, \text{cm} }{ d_1 } $$ $$ \frac{ 1 }{ 2 } = \dfrac{ 0.866\, \text{cm} }{ d_1 } $$ $$ d_1 = \dfrac{ 0.866\, \text{cm} }{ \frac{ 1 }{ 2 } } $$ $$ d_1 = 1.7321\, \text{cm} $$

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