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 $c = 6\, \text{cm}$ 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 $h = 3 \sqrt{ 3 }\, \text{cm}$ and $c = 6\, \text{cm}$ we have:

$$ \left( 3 \sqrt{ 3 }\, \text{cm} \right)^{2} + x^2 = \left( 6\, \text{cm} \right)^{2} $$ $$ x^2 = \left( 6\, \text{cm} \right)^{2} - \left( 3 \sqrt{ 3 }\, \text{cm} \right)^{2} $$ $$ x^2 = 36\, \text{cm}^2 - 27\, \text{cm}^2 $$ $$ x^2 = 9\, \text{cm}^2 $$ $$ x = \sqrt{ 9\, \text{cm}^2 } $$$$ x = 3\, \text{cm} $$

STEP 4: find short base $ b $

To find short base $ b $ use formula:

$$ x = \frac{ a - b } { 2 } $$

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

$$ 3\, \text{cm} = \frac{ 20\, \text{cm} - b } { 2 } $$ $$ 3\, \text{cm} \cdot 2 = 20\, \text{cm} - b $$ $$ 20\, \text{cm} - b = 6\, \text{cm} $$ $$ b = 20\, \text{cm} - 6\, \text{cm} $$ $$ b = 14\, \text{cm} $$

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