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 $ 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 $ and $ c = 7 $ we have:
$$ 6.5778^2 + x^2 = 7^2 $$ $$ x^2 = 7^2 - 6.5778^2 $$ $$ x^2 = 49 - 43.2681 $$ $$ x^2 = 5.7319 $$ $$ x = \sqrt{ 5.7319 } $$$$ x = 2.3941 $$STEP 3: find short base $ b $
To find short base $ b $ use formula:
$$ x = \frac{ a - b } { 2 } $$After substituting $ x = 2.3941 $ and $ a = 22 $ we have:
$$ 2.3941 = \frac{ 22 - b } { 2 } $$ $$ 2.3941 \cdot 2 = 22 - b $$ $$ 22 - b = 4.7883 $$ $$ b = 4.7883 + 22 $$ $$ a = 26.7883 $$