STEP 1: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

After substituting $h = 90\, \text{cm}$ and $a = 120\, \text{cm}$ we have:

$$ \sin \left( \alpha \right) = \dfrac{ 90\, \text{cm} }{ 120\, \text{cm} } $$ $$ \sin \left( \alpha \right) = \frac{ 3 }{ 4 } $$ $$ \alpha = \arcsin\left( \frac{ 3 }{ 4 } \right) $$ $$ \alpha = 48.5904^o $$

STEP 2: find angle $ \beta $

To find angle $ \beta $ use formula:

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

After substituting $ \alpha = 48.5904^o $ we have:

$$ 48.5904^o + \beta = 90^o $$ $$ \beta = 90^o - 48.5904^o $$ $$ \beta = 41.4096^o $$

STEP 3: find diagonal $ d2 $

To find diagonal $ d2 $ use formula:

$$ \sin \left( \frac{ \beta }{ 2 } \right) = \dfrac{ h }{ d_2 } $$

After substituting $\beta = 41.4096^o$ and $h = 90\, \text{cm}$ we have:

$$ \sin \left( \frac{ 41.4096^o }{ 2 } \right) = \dfrac{ h }{ d_2 } $$ $$ \sin( 20.7048 ) = \dfrac{ 90\, \text{cm} }{ d_2 } $$ $$ 0.3536 = \dfrac{ 90\, \text{cm} }{ d_2 } $$ $$ d_2 = \dfrac{ 90\, \text{cm} }{ 0.3536 } $$ $$ d_2 = 254.5584\, \text{cm} $$

Rhombus Calculator