STEP 1: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

After substituting $ \beta = 36^o $ we have:

$$ \alpha + 36^o = 90^o $$ $$ \alpha = 90^o - 36^o $$ $$ \alpha = 54^o $$

STEP 2: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$

After substituting $\alpha = 54^o$ and $d_2 = 9\, \text{cm}$ we have:

$$ \sin \left( \frac{ 54^o }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$ $$ \sin( 27^o ) = \dfrac{ 9\, \text{cm} }{ d_1 } $$ $$ 0.454 = \dfrac{ 9\, \text{cm} }{ d_1 } $$ $$ d_1 = \dfrac{ 9\, \text{cm} }{ 0.454 } $$ $$ d_1 = 19.8242\, \text{cm} $$

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