STEP 1: find side $ x $

To find side $ x $ use formula:

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

After substituting $a = 25.5\, \text{cm}$ and $b = 22\, \text{cm}$ we have:

$$ x = \frac{ 25.5\, \text{cm} - 22\, \text{cm} } { 2 } $$ $$ x = \frac{ 3.5\, \text{cm} } { 2 } $$ $$ x = 1.75\, \text{cm} $$

STEP 2: find height $ h $

To find height $ h $ use Pythagorean Theorem:

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

After substituting $x = 1.75\, \text{cm}$ and $c = 24\, \text{cm}$ we have:

$$ h ^ {\,2} + \left( 1.75\, \text{cm} \right)^{2} = \left( 24\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = \left( 24\, \text{cm} \right)^{2} - \left( 1.75\, \text{cm} \right)^{2} $$ $$ h ^ {\,2} = 576\, \text{cm}^2 - 3.0625\, \text{cm}^2 $$ $$ h ^ {\,2} = 572.9375\, \text{cm}^2 $$ $$ h = \sqrt{ 572.9375\, \text{cm}^2 } $$$$ h = 23.9361\, \text{cm} $$

STEP 3: find angle $ \alpha $

To find angle $ \alpha $ use formula:

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

After substituting $h = 23.9361\, \text{cm}$ and $c = 24\, \text{cm}$ we have:

$$ \sin \left( \alpha \right) = \dfrac{ 23.9361\, \text{cm} }{ 24\, \text{cm} } $$ $$ \sin \left( \alpha \right) = 0.9973 $$ $$ \alpha = \arcsin\left( 0.9973 \right) $$ $$ \alpha = 85.8185^o $$

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