The length of side $BC$ is approximately $2.76 \, \text{cm}$.

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Here are 8 related questions:

1. What if $m\angle C$ had been $104.68^\circ$? How would that change the length of $BC$?
2. How can the Law of Sines be applied in real-life problems involving triangles?
3. What is the relationship between the angles and sides in a triangle?
4. How does the Law of Cosines complement the Law of Sines?
5. What are the differences between solving triangles with and without right angles?
6. How can trigonometric identities help in verifying triangle calculations?
7. Can you always trust the diagram to be drawn to scale in geometric problems?
8. Why is the sum of the angles in a triangle always $180^\circ$?

Tip: When solving triangles, ensure that your angle measurements are accurate to avoid incorrect side lengths.