Find the area $ A $ of a rhombus if side $a = 10$ and angle $\beta = 80^o$.

$A = 17.3648$

STEP 1: find angle $ \alpha $

To find angle $ \alpha $ use formula:

$$ \alpha + \beta = 90^o $$

After substituting $ \beta = 80^o $ we have:

$$ \alpha + 80^o = 90^o $$ $$ \alpha = 90^o - 80^o $$ $$ \alpha = 10^o $$

STEP 2: find area $ A $

To find area $ A $ use formula:

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

After substituting $ a = 10 $ , $ a = 10 $ and $ \alpha = 10^o $ we have:

$$ A = \dfrac{ 10 \cdot 10 \cdot \sin( 10^o ) }{ 1 } $$ $$ A = \dfrac{ 10 \cdot 10 \cdot 0.1736 }{ 1 } $$ $$ A = \dfrac{ 100 \cdot 0.1736 }{ 1 } $$ $$ A = \dfrac{ 17.3648 }{ 1 } $$ $$ A \approx 17.3648 $$

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