Find the angle $ \alpha $ of a rhombus if side $a = 15$ and area $A = 40$.

$\alpha = 10.2403^o$

To find angle $ \alpha $ use formula:

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

After substituting $ A = 40 $ , $ a = 15 $ and $ a = 15 $ we have:

$$ 40 = \dfrac{ 15 \cdot 15 \cdot \sin( \alpha ) }{ 1 } $$ $$ 40 = \dfrac{ 225 \cdot \sin( \alpha ) }{ 1 } $$ $$ 40 \cdot 1 = 225 \cdot \sin( \alpha ) $$ $$ 40 = 225 \cdot \sin( \alpha ) $$ $$ \sin( \alpha ) = \dfrac{ 40 } { 225 } $$ $$ \sin( \alpha ) = \frac{ 8 }{ 45 } $$ $$ \alpha = \arcsin \left( \frac{ 8 }{ 45 } \right)$$ $$ \alpha \approx 10.2403^o $$

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