STEP 1: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

$$ A = \dfrac{ d_1 \cdot d_2 }{ 2 } $$

After substituting $A = 480\, \text{cm}$ and $d_2 = 48\, \text{cm}$ we have:

$$ 480\, \text{cm} = \dfrac{ d_1 \cdot \left( 48\, \text{cm} \right)^{4} }{ 2 } $$$$ 480\, \text{cm} \cdot 2 = d_1 \cdot \left( 48\, \text{cm} \right)^{4} $$$$ 960\, \text{cm} = 48\, \text{cm} \cdot d_1 $$$$ d_1 = \dfrac{ 960\, \text{cm}}{ 48\, \text{cm} } $$$$ d_1 \approx 6.3662 $$

STEP 2: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

After substituting $d_2 = 48\, \text{cm}$ and $d_1 = 6.3662\, \text{cm}^0$ we have:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ 48\, \text{cm} }{ 6.3662 } $$ $$ \sin \left( \frac{ \alpha }{ 2 } \right) = 7.5398\, \text{cm} $$ $$ \frac{ \alpha }{ 2 } = \arcsin\left( 7.5398\, \text{cm} \right) $$

$ \arcsin(7.54) $ is not defined $ \Longrightarrow $ The problem has no solution.

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