Find the angle $ \beta $ of a rhombus if side $a = \frac{ 29 }{ 10 }$ and height $h = \frac{ 5 }{ 4 }$.

$\beta = 64.4668^o$

STEP 1: find angle $ \alpha $

To find angle $ \alpha $ use formula:

$$ \sin \left( \alpha \right) = \dfrac{ h }{ a } $$

After substituting $ h = \frac{ 5 }{ 4 } $ and $ a = \frac{ 29 }{ 10 } $ we have:

$$ \sin \left( \alpha \right) = \dfrac{ \frac{ 5 }{ 4 } }{ \frac{ 29 }{ 10 } } $$ $$ \sin \left( \alpha \right) = \frac{ 25 }{ 58 } $$ $$ \alpha = \arcsin\left( \frac{ 25 }{ 58 } \right) $$ $$ \alpha = 25.5332^o $$

STEP 2: find angle $ \beta $

To find angle $ \beta $ use formula:

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

After substituting $ \alpha = 25.5332^o $ we have:

$$ 25.5332^o + \beta = 90^o $$ $$ \beta = 90^o - 25.5332^o $$ $$ \beta = 64.4668^o $$

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