STEP 1: find side $ x $
To find side $ x $ use formula:
$$ x = \frac{ a - b } { 2 } $$After substituting $ a = 25 $ and $ b = 18 $ we have:
$$ x = \frac{ 25 - 18 } { 2 } $$ $$ x = \frac{ 7 } { 2 } $$ $$ x = \frac{ 7 }{ 2 } $$STEP 2: find side $ c $
To find side $ c $ use Pythagorean Theorem:
$$ h^2 + x^2 = c^2 $$After substituting $ h = 10 $ and $ x = \frac{ 7 }{ 2 } $ we have:
$$ 10^2 + \left(\frac{ 7 }{ 2 }\right)^2 = c^2 $$ $$ 100 + \frac{ 49 }{ 4 } = c^2 $$ $$ c^2 = \frac{ 449 }{ 4 } $$ $$ c = \sqrt{ \frac{ 449 }{ 4 } } $$$$ c = \frac{\sqrt{ 449 }}{ 2 } $$STEP 3: find angle $ \alpha $
To find angle $ \alpha $ use formula:
$$ \sin \left( \alpha \right) = \dfrac{ h }{ c } $$After substituting $ h = 10 $ and $ c = \frac{\sqrt{ 449 }}{ 2 } $ we have:
$$ \sin \left( \alpha \right) = \dfrac{ 10 }{ \frac{\sqrt{ 449 }}{ 2 } } $$ $$ \sin \left( \alpha \right) = \frac{ 20 \sqrt{ 449}}{ 449 } $$ $$ \alpha = \arcsin\left( \frac{ 20 \sqrt{ 449}}{ 449 } \right) $$ $$ \alpha = 70.71^o $$STEP 4: find angle $ \beta $
To find angle $ \beta $ use formula:
$$ \alpha + \beta = 180^o $$After substituting $ \alpha = 70.71^o $ we have:
$$ 70.71^o + \beta = 180^o $$ $$ \beta = 180^o - 70.71^o $$ $$ \beta = 109.29^o $$