Let's solve the triangle using the Law of Sines.

We are given:

• $A = 34.9^\circ$
• $a = 27$
• $b = 32$

Step 1: Use the Law of Sines

The Law of Sines states: $\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$ Using the known values, we can set up the equation: $\frac{\sin 34.9^\circ}{27} = \frac{\sin B}{32}$ Solving for $\sin B$: $\sin B = \frac{32 \cdot \sin 34.9^\circ}{27}$

Let's calculate $\sin B$ first.