STEP 1: find height $ h $

To find height $ h $ use formula:

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

After substituting $\alpha = 30^o$ and $a = 5.4\, \text{cm}$ we have:

$$ \sin( 30^o ) = \dfrac{ h }{ 5.4 } $$ $$ \frac{ 1 }{ 2 } = \dfrac{ h }{ 5.4 } $$$$ h = \frac{ 1 }{ 2 } \cdot 5.4 $$$$ h = 2.7 $$

STEP 2: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

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

After substituting $\alpha = 30^o$ and $h = 2.7\, \text{cm}$ we have:

$$ \sin \left( \frac{ 30^o }{ 2 } \right) = \dfrac{ h }{ d_1 } $$ $$ \sin( 15^o ) = \dfrac{ 2.7\, \text{cm} }{ d_1 } $$ $$ 0.2588 = \dfrac{ 2.7\, \text{cm} }{ d_1 } $$ $$ d_1 = \dfrac{ 2.7\, \text{cm} }{ 0.2588 } $$ $$ d_1 = 10.432\, \text{cm} $$

Rhombus Calculator