Chapter 8 - Applications of Trigonometric Functions - 8.2 The Law of Sines - 8.2 Assess Your Understanding - Page 530: 21

$B= 40^\circ$ $a \approx5.64$ $b \approx3.86$

Step 1. Using the given conditions, we have $B=180-110-30=40^\circ$ Step 2. Using the Law of Sines, we have $\frac{a}{sin110^\circ}=\frac{b}{sin40^\circ}=\frac{3}{sin30^\circ}$ Step 3. Thus $a=\frac{3sin110^\circ}{sin30^\circ} \approx5.64$ and $b=\frac{3sin40^\circ}{sin30^\circ}\approx3.86$