STEP 1: find angle $ \alpha $
To find angle $ \alpha $ use formula:
$$ \alpha + \beta = 180^o $$After substituting $ \beta = 45^o $ we have:
$$ \alpha + 45^o = 180^o $$ $$ \alpha = 180^o - 45^o $$ $$ \alpha = 135^o $$STEP 2: find height $ h $
To find height $ h $ use formula:
$$ \sin \left( \alpha \right) = \dfrac{ h }{ c } $$After substituting $ \alpha = 135^o $ and $ c = 27 $ we have:
$$ \sin( 135^o ) = \dfrac{ h }{ 27 } $$ $$ - \frac{\sqrt{ 2 }}{ 2 } = \dfrac{ h }{ 27 } $$$$ h = - \frac{\sqrt{ 2 }}{ 2 } \cdot 27 $$$$ h = -27 \frac{\sqrt{ 2 }}{ 2 } $$The result has to be greater than zero. $ \Longrightarrow $ The problem has no solution.