Find the angle $ \beta $ of a rhombus if diagonal $d_1 = 30$ and diagonal $d_2 = 16$.

$\beta = 25.5381^o$

STEP 1: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

After substituting $ d_2 = 16 $ and $ d_1 = 30 $ we have:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ 16 }{ 30 } $$ $$ \sin \left( \frac{ \alpha }{ 2 } \right) = \frac{ 8 }{ 15 } $$ $$ \frac{ \alpha }{ 2 } = \arcsin\left( \frac{ 8 }{ 15 } \right) $$ $$ \frac{ \alpha }{ 2 } = 32.231^o $$$$ \alpha = 32.231^o \cdot 2 $$$$ \alpha = 64.4619^o $$

STEP 2: find angle $ \beta $

To find angle $ \beta $ use formula:

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

After substituting $ \alpha = 64.4619^o $ we have:

$$ 64.4619^o + \beta = 90^o $$ $$ \beta = 90^o - 64.4619^o $$ $$ \beta = 25.5381^o $$

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