#### Answer

The sum of $A$ and $B$ is greater than $180^{\circ}$, so no triangle exists satisfying the given values.

#### Work Step by Step

$A = 103^{\circ}20'$
$a = 14.6~ft$
$b = 20.4~ft$
Since $b \gt a$, the angle which subtends $b$ must be larger than the angle which subtends $a$. That is: $B \gt A$.
However, then the sum of $A$ and $B$ is greater than $180^{\circ}$, so no triangle exists satisfying the given values.