STEP 1: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

After substituting $d_2 = 7\, \text{cm}$ and $d_1 = 14\, \text{cm}$ we have:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ 7\, \text{cm} }{ 14\, \text{cm} } $$ $$ \sin \left( \frac{ \alpha }{ 2 } \right) = \frac{ 1 }{ 2 } $$ $$ \frac{ \alpha }{ 2 } = \arcsin\left( \frac{ 1 }{ 2 } \right) $$ $$ \frac{ \alpha }{ 2 } = 30^o $$$$ \alpha = 30^o \cdot 2 $$$$ \alpha = 60^o $$

STEP 2: find height $ h $

To find height $ h $ use formula:

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

After substituting $\alpha = 60^o$ and $d_1 = 14\, \text{cm}$ we have:

$$ \sin \left( \frac{ 60^o }{ 2 } \right) = \dfrac{ h }{ d_1 } $$ $$ \sin( 30 ) = \dfrac{ h }{ 14 } $$ $$ \frac{ 1 }{ 2 } = \dfrac{ h }{ 14 } $$$$ h = \frac{ 1 }{ 2 } \cdot 14 $$$$ h = 7 $$

STEP 3: find incircle radius $ r $

To find incircle radius $ r $ use formula:

$$ h = 2 \cdot r $$

After substituting $h = 7\, \text{cm}$ we have:

$$ 7\, \text{cm} = 2 \cdot r $$ $$ r = \dfrac{ 7\, \text{cm} }{ 2 } $$ $$ r = \frac{ 7 }{ 2 }\, \text{cm} $$

Rhombus Calculator