STEP 1: find angle $ \beta $

To find angle $ \beta $ use formula:

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

After substituting $ \alpha = 36.5^o $ we have:

$$ 36.5^o + \beta = 90^o $$ $$ \beta = 90^o - 36.5^o $$ $$ \beta = 53.5^o $$

STEP 2: find height $ h $

To find height $ h $ use formula:

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

After substituting $\alpha = 36.5^o$ and $a = 338\, \text{cm}$ we have:

$$ \sin( 36.5^o ) = \dfrac{ h }{ 338 } $$ $$ 0.5948 = \dfrac{ h }{ 338 } $$$$ h = 0.5948 \cdot 338 $$$$ h = 201.0501 $$

STEP 3: find diagonal $ d2 $

To find diagonal $ d2 $ use formula:

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

After substituting $\beta = 53.5^o$ and $h = 201.0501\, \text{cm}$ we have:

$$ \sin \left( \frac{ 53.5^o }{ 2 } \right) = \dfrac{ h }{ d_2 } $$ $$ \sin( 26.75 ) = \dfrac{ 201.0501\, \text{cm} }{ d_2 } $$ $$ 0.4501 = \dfrac{ 201.0501\, \text{cm} }{ d_2 } $$ $$ d_2 = \dfrac{ 201.0501\, \text{cm} }{ 0.4501 } $$ $$ d_2 = 446.6803\, \text{cm} $$

Rhombus Calculator