To solve the problem, we will apply the triangle inequality properties and the law of cosines to determine the relative sizes of the angles in this triangle.

Given:

• Side opposite $\angle A = 16$ (BC)
• Side opposite $\angle B = 10$ (AC)
• Side opposite $\angle C = 14$ (AB)

Key Principle:

• In a triangle, the larger the side opposite an angle, the larger the angle itself.

Step-by-Step Solution:

1. Ordering by sides:

   • $\angle A$ is opposite the largest side (16), so it is the largest angle.
   • $\angle B$ is opposite the smallest side (10), so it is the smallest angle.
   • $\angle C$ is opposite the medium side (14), so it is the middle angle.

2. Final order of angles from smallest to largest: $\angle B < \angle C < \angle A$

Would you like me to show calculations using the law of cosines to confirm the angle measures explicitly?