STEP 1: find side $ x $
To find side $ x $ use formula:
$$ x = \frac{ a - b } { 2 } $$After substituting $ a = 300 $ and $ b = \frac{ 1 }{ 20 } $ we have:
$$ x = \frac{ 300 - \frac{ 1 }{ 20 } } { 2 } $$ $$ x = \frac{ \frac{ 5999 }{ 20 } } { 2 } $$ $$ x = \frac{ 5999 }{ 40 } $$STEP 2: find side $ c $
To find side $ c $ use Pythagorean Theorem:
$$ h^2 + x^2 = c^2 $$After substituting $ h = 8333 $ and $ x = \frac{ 5999 }{ 40 } $ we have:
$$ 8333^2 + \left(\frac{ 5999 }{ 40 }\right)^2 = c^2 $$ $$ 69438889 + \frac{ 35988001 }{ 1600 } = c^2 $$ $$ c^2 = \frac{ 111138210401 }{ 1600 } $$ $$ c = \sqrt{ \frac{ 111138210401 }{ 1600 } } $$$$ c = \frac{\sqrt{ 111138210401 }}{ 40 } $$STEP 3: find angle $ \alpha $
To find angle $ \alpha $ use formula:
$$ \sin \left( \alpha \right) = \dfrac{ h }{ c } $$After substituting $ h = 8333 $ and $ c = \frac{\sqrt{ 111138210401 }}{ 40 } $ we have:
$$ \sin \left( \alpha \right) = \dfrac{ 8333 }{ \frac{\sqrt{ 111138210401 }}{ 40 } } $$ $$ \sin \left( \alpha \right) = \frac{ 333320 \sqrt{ 111138210401}}{ 111138210401 } $$ $$ \alpha = \arcsin\left( \frac{ 333320 \sqrt{ 111138210401}}{ 111138210401 } \right) $$ $$ \alpha = 88.9689^o $$STEP 4: find angle $ \beta $
To find angle $ \beta $ use formula:
$$ \alpha + \beta = 180^o $$After substituting $ \alpha = 88.9689^o $ we have:
$$ 88.9689^o + \beta = 180^o $$ $$ \beta = 180^o - 88.9689^o $$ $$ \beta = 91.0311^o $$