STEP 1: find side $ a $
To find side $ a $ use formula:
$$ A = \dfrac{ a \cdot b }{ 2 } $$After substituting $ A = 90 $ and $ b = 4 $ we have:
$$ 90 = \dfrac{ a \cdot 4 }{ 2 } $$$$ 90 \cdot 2 = a \cdot 4 $$$$ 180 = 4 \cdot a $$$$ a = \dfrac{ 180}{ 4 } $$$$ a = 45 $$STEP 2: find angle $ \beta $
To find angle $ \beta $ use formula:
$$ \tan \left( \beta \right) = \dfrac{ b }{ a } $$After substituting $ b = 4 $ and $ a = 45 $ we have:
$$ \tan \left( \beta \right) = \dfrac{ 4 }{ 45 } $$ $$ \tan \left( \beta \right) = \frac{ 4 }{ 45 } $$ $$ \beta = \arctan\left( \frac{ 4 }{ 45 } \right) $$ $$ \beta = 5.0796^o $$