Answer
$a \approx 20.38$
$b \approx 17.71$
$B= 41^{\circ}$
Work Step by Step
Here, $\sin A=\dfrac{a}{c}$
This gives: $\sin 49^{\circ}=\dfrac{a}{27} \implies a \approx 20.38$
Now, $\sin B=\dfrac{b}{c}$
This gives: $\sin 41^{\circ}=\dfrac{b}{27} \implies b \approx 17.71$
Since the sum of a triangle is $180^{\circ}$ and the right angle is $90^{\circ}$:
$ B=180^{\circ}-49^{\circ}-90^{\circ}=41^{\circ}$
