Answer
$b \approx 55.98$
and $c \approx 57.96$
$ A=15^{\circ}$
Work Step by Step
Here, $\tan B=\dfrac{b}{a}$
This gives: $\tan 75^{\circ}=\dfrac{b}{15} \implies b \approx 55.98$
Now, $\sin A=\dfrac{a}{c}$
This gives: $\sin 75^{\circ}=\dfrac{15}{c} \implies c \approx 57.96$
Since the sum of a triangle is $180^{\circ}$ and the right angle is $90^{\circ}$:
$ A=180^{\circ}-75^{\circ}-90^{\circ}=15^{\circ}$
