STEP 1: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

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

After substituting $d_2 = 7.9375\, \text{cm}$ and $a = 4.125\, \text{cm}$ we have:

$$ d_1 ^ {\,2} + \left( 7.9375\, \text{cm} \right)^{2} = 4 \cdot \left( 4.125\, \text{cm} \right)^{2} $$ $$ d_1 ^ {\,2} + 63.0039\, \text{cm}^2 = = 68.0625\, \text{cm}^2 $$ $$ d_1 ^ {\,2} = = 68.0625\, \text{cm}^2 - 63.0039\, \text{cm}^2 $$ $$ d_1 ^ {\,2} = 5.0586\, \text{cm}^2 $$ $$ d_1 = \sqrt{ 5.0586\, \text{cm}^2 } $$$$ d_1 = 2.2491\, \text{cm} $$

STEP 2: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

After substituting $d_2 = 7.9375\, \text{cm}$ and $d_1 = 2.2491\, \text{cm}$ we have:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ 7.9375\, \text{cm} }{ 2.2491\, \text{cm} } $$ $$ \sin \left( \frac{ \alpha }{ 2 } \right) = 3.5291 $$ $$ \frac{ \alpha }{ 2 } = \arcsin\left( 3.5291 \right) $$

$ \arcsin(3.529) $ is not defined $ \Longrightarrow $ The problem has no solution.

Rhombus Calculator