STEP 1: find angle $ \alpha $
To find angle $ \alpha $ use formula:
$$ \alpha + \beta = 180^o $$After substituting $ \beta = \frac{ 226051 }{ 2000 }^o $ we have:
$$ \alpha + \frac{ 226051 }{ 2000 }^o = 180^o $$ $$ \alpha = 180^o - \frac{ 226051 }{ 2000 }^o $$ $$ \alpha = \frac{ 133949 }{ 2000 }^o $$STEP 2: find side $ c $
To find side $ c $ use formula:
$$ \sin \left( \alpha \right) = \dfrac{ h }{ c } $$After substituting $ \alpha = \frac{ 133949 }{ 2000 }^o $ and $ h = 4 $ we have:
$$ \sin( \frac{ 133949 }{ 2000 }^o ) = \dfrac{ 4 }{ c } $$ $$ 0.9203 = \dfrac{ 4 }{ c } $$ $$ c = \dfrac{ 4 }{ 0.9203 } $$ $$ c = 4.3463 $$STEP 3: find side $ x $
To find side $ x $ use Pythagorean Theorem:
$$ h^2 + x^2 = c^2 $$After substituting $ h = 4 $ and $ c = 4.3463 $ we have:
$$ 4^2 + x^2 = 4.3463^2 $$ $$ x^2 = 4.3463^2 - 4^2 $$ $$ x^2 = 18.89 - 16 $$ $$ x^2 = 2.89 $$ $$ x = \sqrt{ 2.89 } $$$$ x = 1.7 $$STEP 4: find short base $ b $
To find short base $ b $ use formula:
$$ x = \frac{ a - b } { 2 } $$After substituting $ x = 1.7 $ and $ a = 11 $ we have:
$$ 1.7 = \frac{ 11 - b } { 2 } $$ $$ 1.7 \cdot 2 = 11 - b $$ $$ 11 - b = 3.4 $$ $$ b = 3.4 + 11 $$ $$ a = 14.4 $$