This question involves the relationship between the angles and sides of a triangle based on the angle-side inequality theorem.

Given:

• Triangle $\triangle ABC$, with angle measures $\angle C < \angle B < \angle A$.

Key Concept:

In a triangle, the larger the angle, the longer the side opposite to it. This means that the side opposite the largest angle will be the longest, and the side opposite the smallest angle will be the shortest.

Applying to $\triangle ABC$:

• $\angle C < \angle B < \angle A$
  • Since $\angle C$ is the smallest, the side opposite $\angle C$ (which is $AB$) will be the shortest.
  • $\angle A$ is the largest, so the side opposite $\angle A$ (which is $BC$) will be the longest.
  • $\angle B$ is in the middle, so the side opposite $\angle B$ (which is $AC$) will have a length between $AB$ and $BC$.

Thus, the order of the sides will be: $AB < AC < BC$

Correct Answer:

The second option: AC < AB < BC

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the angle-side relationship theorem in triangles?
2. Can the triangle inequality theorem be applied to this problem?
3. How can we prove that $AB < AC < BC$ using the Law of Sines?
4. What happens if two angles are equal in a triangle? How does this affect the side lengths?
5. How do angle bisectors affect side length comparisons in a triangle?

Tip: Always remember that in a triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle.