Find the diagonal $ d_1 $ of a rhombus if side $a = \frac{ 5 }{ 2 }$ and angle $\alpha = 70^o$.

$d_1 = 4.0958$

STEP 1: find height $ h $

To find height $ h $ use formula:

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

After substituting $ \alpha = 70^o $ and $ a = \frac{ 5 }{ 2 } $ we have:

$$ \sin( 70^o ) = \dfrac{ h }{ \frac{ 5 }{ 2 } } $$ $$ 0.9397 = \dfrac{ h }{ \frac{ 5 }{ 2 } } $$$$ h = 0.9397 \cdot \frac{ 5 }{ 2 } $$$$ h = 2.3492 $$

STEP 2: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

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

After substituting $ \alpha = 35^o $ and $ h = 2.3492 $ we have:

$$ \sin \left( \frac{ 70^o }{ 2 } \right) = \dfrac{ h }{ } $$ $$ \sin( 35^o ) = \dfrac{ 2.3492 }{ d_1 } $$ $$ 0.5736 = \dfrac{ 2.3492 }{ d_1 } $$ $$ d_1 = \dfrac{ 2.3492 }{ 0.5736 } $$ $$ d_1 = 4.0958 $$

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