Find the angle $ \beta $ of a rhombus if side $a = \frac{ 181 }{ 100 }$ and height $h = \frac{ 179 }{ 100 }$.

$\beta = 8.5254^o$

STEP 1: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

After substituting $ h = \frac{ 179 }{ 100 } $ and $ a = \frac{ 181 }{ 100 } $ we have:

$$ \sin \left( \alpha \right) = \dfrac{ \frac{ 179 }{ 100 } }{ \frac{ 181 }{ 100 } } $$ $$ \sin \left( \alpha \right) = \frac{ 179 }{ 181 } $$ $$ \alpha = \arcsin\left( \frac{ 179 }{ 181 } \right) $$ $$ \alpha = 81.4746^o $$

STEP 2: find angle $ \beta $

To find angle $ \beta $ use formula:

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

After substituting $ \alpha = 81.4746^o $ we have:

$$ 81.4746^o + \beta = 90^o $$ $$ \beta = 90^o - 81.4746^o $$ $$ \beta = 8.5254^o $$

Rhombus Calculator