STEP 1: find angle $ \gamma $

To find angle $ \gamma $ use The Law of Sines:

$$ \dfrac{ \sin( \beta )} { b } = \dfrac{ \sin( \gamma )} { c } $$

After substituting $b = 14\, \text{cm}$, $\beta = 154^o$ and $c = 16\, \text{cm}$ we have:

$$ \dfrac{ \sin( 154^o )} { 14\, \text{cm} } = \dfrac{ \sin( \gamma )} { 16\, \text{cm} } $$ $$ \dfrac{ 0.4384 } { 14\, \text{cm} } = \dfrac{ \sin( \gamma ) } { 16\, \text{cm} } $$ $$ \sin( \gamma ) \cdot 14\, \text{cm} = 0.4384 \cdot 16\, \text{cm} $$ $$ \sin( \gamma ) \cdot 14\, \text{cm} = 7.0139\, \text{cm} $$ $$ \sin( \gamma ) = \dfrac{ 7.0139\, \text{cm} }{ 14\, \text{cm} } $$ $$ \sin( \gamma ) = 0.501 $$ $$ \gamma = \arcsin{ 0.501 } $$ $$ \gamma \approx 30.0659^o $$

STEP 2: find angle $ \alpha $

To find angle $ \alpha $ use formula:

$$ \alpha + \beta + \gamma = 180^o $$

After substituting $\beta = 154^o$ and $\gamma = 30.0659^o$ we have:

$$ \alpha + 154^o + 30.0659^o = 180^o $$ $$ \alpha + 184.0659^o = 180^o $$ $$ \alpha = 180^o - 184.0659^o $$ $$ \alpha = -4.0659^o $$

The result has to be greater than zero. $ \Longrightarrow $ The problem has no solution.

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