The problem involves identifying the correct descriptions of the sides of a right triangle $\triangle ABC$ relative to angle $\angle B$.

Here’s the solution:

1. Understand the problem:
   In a right triangle:

   • The hypotenuse is the side opposite the right angle ($\angle C$), which is the longest side ($AB$ in this case).
   • The opposite side relative to an angle (e.g., $\angle B$) is the side directly across from the angle.
   • The adjacent side relative to an angle (e.g., $\angle B$) is the side next to the angle that is not the hypotenuse.

2. Analysis of Tomas’s description:

   • Tomas states that:
     • $AB$ is the hypotenuse (correct).
     • $AC$ is the opposite side to $\angle B$ (incorrect).
       $AC$ is the side next to $\angle B$, so it is the adjacent side.
     • $BC$ is the adjacent side to $\angle B$ (incorrect).
       $BC$ is directly across from $\angle B$, so it is the opposite side.

3. Analysis of Iliana’s description:

   • Iliana states that:
     • $AB$ is the hypotenuse (correct).
     • $BC$ is the opposite side to $\angle B$ (correct).
       $BC$ is the side directly across from $\angle B$.
     • $AC$ is the adjacent side to $\angle B$ (correct).
       $AC$ is next to $\angle B$ but not the hypotenuse.

4. Conclusion:
   Iliana’s description is correct. The correct answer is:
   "Iliana is correct; $BC$ is opposite $\angle B$ and $AC$ is adjacent to $\angle B$."

Would you like a breakdown of this explanation or more examples of this concept?

Related Questions:

1. What are the definitions of hypotenuse, adjacent, and opposite sides in a triangle?
2. How does the orientation of the triangle affect the naming of sides?
3. What are the trigonometric ratios ($\sin$, $\cos$, $\tan$) relative to an angle in a right triangle?
4. How can we find the length of a side in a triangle using trigonometry?
5. How does the Pythagorean theorem relate to the hypotenuse?

Tip:

To avoid confusion when identifying sides in a triangle, always start by marking the hypotenuse (longest side) first. Then consider the angle of interest to classify the opposite and adjacent sides.