STEP 1: find side $ a $

To find side $ a $ use formula:

$$ A = a \cdot h $$

After substituting $A = 20\, \text{cm}$ and $h = 3\, \text{cm}$ we have:

$$ 20\, \text{cm} = 3\, \text{cm} \cdot a $$$$ a = \dfrac{ 20\, \text{cm}}{ 3\, \text{cm} } $$$$ a \approx 2.1221 $$

STEP 2: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

After substituting $h = 3\, \text{cm}$ and $a = 2.1221\, \text{cm}^0$ we have:

$$ \sin \left( \alpha \right) = \dfrac{ 3\, \text{cm} }{ 2.1221 } $$ $$ \sin \left( \alpha \right) = 1.4137\, \text{cm} $$ $$ \alpha = \arcsin\left( 1.4137\, \text{cm} \right) $$

$ \arcsin(1.414) $ is not defined $ \Longrightarrow $ The problem has no solution.

Rhombus Calculator