Find the angle $ \alpha $ of a rhombus if side $a = 16$ and area $A = 214$.

$\alpha = 56.7136^o$

To find angle $ \alpha $ use formula:

$$ A = \dfrac{ a \cdot a \cdot \sin( \alpha ) }{ 1 } $$

After substituting $ A = 214 $ , $ a = 16 $ and $ a = 16 $ we have:

$$ 214 = \dfrac{ 16 \cdot 16 \cdot \sin( \alpha ) }{ 1 } $$ $$ 214 = \dfrac{ 256 \cdot \sin( \alpha ) }{ 1 } $$ $$ 214 \cdot 1 = 256 \cdot \sin( \alpha ) $$ $$ 214 = 256 \cdot \sin( \alpha ) $$ $$ \sin( \alpha ) = \dfrac{ 214 } { 256 } $$ $$ \sin( \alpha ) = \frac{ 107 }{ 128 } $$ $$ \alpha = \arcsin \left( \frac{ 107 }{ 128 } \right)$$ $$ \alpha \approx 56.7136^o $$

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