STEP 1: find height $ h $

To find height $ h $ use formula:

$$ \sin \left( \alpha \right) = \dfrac{ h }{ c } $$

After substituting $\alpha = 70^o$ and $c = 7\, \text{cm}$ we have:

$$ \sin( 70^o ) = \dfrac{ h }{ 7 } $$ $$ 0.9397 = \dfrac{ h }{ 7 } $$$$ h = 0.9397 \cdot 7 $$$$ h = 6.5778 $$

STEP 2: find side $ x $

To find side $ x $ use Pythagorean Theorem:

$$ h^2 + x^2 = c^2 $$

After substituting $h = 6.5778\, \text{cm}$ and $c = 7\, \text{cm}$ we have:

$$ \left( 6.5778\, \text{cm} \right)^{2} + x^2 = \left( 7\, \text{cm} \right)^{2} $$ $$ x^2 = \left( 7\, \text{cm} \right)^{2} - \left( 6.5778\, \text{cm} \right)^{2} $$ $$ x^2 = 49\, \text{cm}^2 - 43.2681\, \text{cm}^2 $$ $$ x^2 = 5.7319\, \text{cm}^2 $$ $$ x = \sqrt{ 5.7319\, \text{cm}^2 } $$$$ x = 2.3941\, \text{cm} $$

STEP 3: find short base $ b $

To find short base $ b $ use formula:

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

After substituting $x = 2.3941\, \text{cm}$ and $a = 22\, \text{cm}$ we have:

$$ 2.3941\, \text{cm} = \frac{ 22\, \text{cm} - b } { 2 } $$ $$ 2.3941\, \text{cm} \cdot 2 = 22\, \text{cm} - b $$ $$ 22\, \text{cm} - b = 4.7883\, \text{cm} $$ $$ b = 22\, \text{cm} - 4.7883\, \text{cm} $$ $$ b = 17.2117\, \text{cm} $$

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