STEP 1: find angle $ \alpha $
To find angle $ \alpha $ use formula:
$$ \alpha + \beta = 180^o $$After substituting $ \beta = 120^o $ we have:
$$ \alpha + 120^o = 180^o $$ $$ \alpha = 180^o - 120^o $$ $$ \alpha = 60^o $$STEP 2: find height $ h $
To find height $ h $ use formula:
$$ \sin \left( \alpha \right) = \dfrac{ h }{ c } $$After substituting $ \alpha = 60^o $ and $ c = 6 $ we have:
$$ \sin( 60^o ) = \dfrac{ h }{ 6 } $$ $$ \frac{\sqrt{ 3 }}{ 2 } = \dfrac{ h }{ 6 } $$$$ h = \frac{\sqrt{ 3 }}{ 2 } \cdot 6 $$$$ h = 3 \sqrt{ 3 } $$STEP 3: find side $ x $
To find side $ x $ use Pythagorean Theorem:
$$ h^2 + x^2 = c^2 $$After substituting $ h = 3 \sqrt{ 3 } $ and $ c = 6 $ we have:
$$ \left(3 \sqrt{ 3 }\right)^2 + x^2 = 6^2 $$ $$ x^2 = 6^2 - \left(3 \sqrt{ 3 }\right)^2 $$ $$ x^2 = 36 - 27 $$ $$ x^2 = 9 $$ $$ x = \sqrt{ 9 } $$$$ x = 3 $$STEP 4: find short base $ b $
To find short base $ b $ use formula:
$$ x = \frac{ a - b } { 2 } $$After substituting $ x = 3 $ and $ a = 20 $ we have:
$$ 3 = \frac{ 20 - b } { 2 } $$ $$ 3 \cdot 2 = 20 - b $$ $$ 20 - b = 6 $$ $$ b = 6 + 20 $$ $$ a = 26 $$