To solve the triangle using the Law of Sines, we start by finding the measure of angle $A$.

First, we use the fact that the sum of the angles in a triangle is always 180 degrees: $A + B + C = 180^\circ$

Given: $B = 39.78^\circ$ $C = 32.49^\circ$

We can find $A$ by subtracting the sum of $B$ and $C$ from 180 degrees: $A = 180^\circ - B - C$ $A = 180^\circ - 39.78^\circ - 32.49^\circ$ $A = 180^\circ - 72.27^\circ$ $A = 107.73^\circ$

Therefore, the measure of angle $A$ is: $A = 107.73^\circ$

So the correct choice is: A. $A = 107.73$ degrees

Would you like the detailed steps for finding the lengths of the other sides using the Law of Sines, or do you have any other questions?

Here are 5 questions you might consider asking:

1. How do you use the Law of Sines to find the length of side $a$?
2. Can you explain the Law of Cosines and when to use it?
3. What is the formula for the Law of Sines?
4. How do you solve a triangle given two sides and an included angle?
5. What are the possible scenarios for the number of solutions in a triangle problem?

Tip: Always double-check your angle measures to ensure they sum to 180 degrees in a triangle.