Question

two students describe the sides of right triangle abc in relation to ∠b.
tomas
ab is the hypotenuse.
ac is the opposite side.
bc is the adjacent side.
iliana
ab is the hypotenuse.
bc is the opposite side
ac is the adjacent side.
who is correct? explain.
tomas is correct; ac is opposite ∠b and bc is adjacent to ∠b
iliana is correct; bc is opposite ∠b and ac is adjacent to ∠b.
both are correct because both ac and bc are opposite ∠b.
neither is correct because neither ac nor bc is opposite ∠b.

Explanation:

In right triangle ABC (right-angled at C), the hypotenuse is always the side opposite the right angle, so $\overline{AB}$ is correctly identified as the hypotenuse by both. For $\angle B$:

1. The opposite side is the side that does not form the angle, which is $\overline{AC}$.
2. The adjacent side is the side that forms the angle (excluding the hypotenuse), which is $\overline{BC}$.

This matches Tomas's descriptions.

Answer:

Tomas is correct; $\overline{AC}$ is opposite $\angle B$ and $\overline{BC}$ is adjacent to $\angle B$.