STEP 1: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

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

After substituting $d_2 = 11\, \text{cm}$ and $a = 14.12\, \text{cm}$ we have:

$$ d_1 ^ {\,2} + \left( 11\, \text{cm} \right)^{2} = 4 \cdot \left( 14.12\, \text{cm} \right)^{2} $$ $$ d_1 ^ {\,2} + 121\, \text{cm}^2 = = 797.4976\, \text{cm}^2 $$ $$ d_1 ^ {\,2} = = 797.4976\, \text{cm}^2 - 121\, \text{cm}^2 $$ $$ d_1 ^ {\,2} = 676.4976\, \text{cm}^2 $$ $$ d_1 = \sqrt{ 676.4976\, \text{cm}^2 } $$$$ d_1 = 26.0096\, \text{cm} $$

STEP 2: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

After substituting $d_2 = 11\, \text{cm}$ and $d_1 = 26.0096\, \text{cm}$ we have:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ 11\, \text{cm} }{ 26.0096\, \text{cm} } $$ $$ \sin \left( \frac{ \alpha }{ 2 } \right) = 0.4229 $$ $$ \frac{ \alpha }{ 2 } = \arcsin\left( 0.4229 \right) $$ $$ \frac{ \alpha }{ 2 } = 25.0192^o $$$$ \alpha = 25.0192^o \cdot 2 $$$$ \alpha = 50.0383^o $$

Rhombus Calculator