STEP 1: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

$$ d_1^2 + d_2^2 = 4 \cdot a^2 $$

After substituting $d_2 = 3\, \text{cm}$ and $a = 3 \sqrt{ 5 }\, \text{cm}$ we have:

$$ d_1 ^ {\,2} + \left( 3\, \text{cm} \right)^{2} = 4 \cdot \left( 3 \sqrt{ 5 }\, \text{cm} \right)^{2} $$ $$ d_1 ^ {\,2} + 9\, \text{cm}^2 = = 180\, \text{cm}^2 $$ $$ d_1 ^ {\,2} = = 180\, \text{cm}^2 - 9\, \text{cm}^2 $$ $$ d_1 ^ {\,2} = 171\, \text{cm}^2 $$ $$ d_1 = \sqrt{ 171\, \text{cm}^2 } $$$$ d_1 = 3 \sqrt{ 19 }\, \text{cm} $$

STEP 2: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

After substituting $d_2 = 3\, \text{cm}$ and $d_1 = 3 \sqrt{ 19 }\, \text{cm}$ we have:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ 3\, \text{cm} }{ 3 \sqrt{ 19 }\, \text{cm} } $$ $$ \sin \left( \frac{ \alpha }{ 2 } \right) = \frac{\sqrt{ 19 }}{ 19 } $$ $$ \frac{ \alpha }{ 2 } = \arcsin\left( \frac{\sqrt{ 19 }}{ 19 } \right) $$ $$ \frac{ \alpha }{ 2 } = 13.2627^o $$$$ \alpha = 13.2627^o \cdot 2 $$$$ \alpha = 26.5254^o $$

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