Find the angle $ \alpha $ of a rhombus if diagonal $d_1 = 15$ and diagonal $d_2 = \frac{ 66 }{ 5 }$.

$\alpha = 123.2847^o$

To find angle $ \alpha $ use formula:

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

After substituting $ d_2 = \frac{ 66 }{ 5 } $ and $ d_1 = 15 $ we have:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ \frac{ 66 }{ 5 } }{ 15 } $$ $$ \sin \left( \frac{ \alpha }{ 2 } \right) = \frac{ 22 }{ 25 } $$ $$ \frac{ \alpha }{ 2 } = \arcsin\left( \frac{ 22 }{ 25 } \right) $$ $$ \frac{ \alpha }{ 2 } = 61.6424^o $$$$ \alpha = 61.6424^o \cdot 2 $$$$ \alpha = 123.2847^o $$

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