Find the side $ a $ of a rhombus if diagonal $d_1 = 35$ and angle $\alpha = \frac{ 49017 }{ 1000 }^o$.

$a = 19.2329$

STEP 1: find height $ h $

To find height $ h $ use formula:

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

After substituting $ \alpha = \frac{ 49017 }{ 2000 }^o $ and $ d_1 = 35 $ we have:

$$ \sin \left( \frac{ \frac{ 49017 }{ 1000 }^o }{ 2 } \right) = \dfrac{ h }{ 35 } $$ $$ \sin( \frac{ 49017 }{ 2000 }^o ) = \dfrac{ h }{ 35 } $$ $$ 0.4148 = \dfrac{ h }{ 35 } $$$$ h = 0.4148 \cdot 35 $$$$ h = 14.519 $$

STEP 2: find side $ a $

To find side $ a $ use formula:

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

After substituting $ \alpha = \frac{ 49017 }{ 1000 }^o $ and $ h = 14.519 $ we have:

$$ \sin( \frac{ 49017 }{ 1000 }^o ) = \dfrac{ 14.519 }{ a } $$ $$ 0.7549 = \dfrac{ 14.519 }{ a } $$ $$ a = \dfrac{ 14.519 }{ 0.7549 } $$ $$ a = 19.2329 $$

Rhombus Calculator