Answer
A has two possible values when $5 \lt b \lt 10$
Work Step by Step
The sum of the three angles in the triangle is $180^{\circ}$. Since $B = 30^{\circ},$ then $0^{\circ} \lt A \lt 150^{\circ}$
We know that $sin~\theta = sin~(180^{\circ}-\theta)$.
Therefore, the angle $A$ has two possible values when $30^{\circ} \lt A \lt 90^{\circ}$ or $90^{\circ} \lt A \lt 150^{\circ}$
Then $0.5 \lt sin~A \lt 1$
We can use the law of sines to find $b$:
$\frac{a}{sin~A} = \frac{b}{sin~B}$
$b = \frac{a~sin~B}{sin~A}$
$b = \frac{(10)~sin~30^{\circ}}{sin~A}$
$b = \frac{5}{sin~A}$
If $0.5 \lt sin~A \lt 1$ then $5 \lt b \lt 10$
Therefore, A has two possible values when $5 \lt b \lt 10$
