Question

two students describe the sides of right triangle abc in relation to ∠b.

tomas	iliana
ac is the opposite side.	bc is the opposite side.
bc is the adjacent side.	ac is the adjacent side.

who is correct? explain.
iliana is correct; bc is opposite ∠b and ac is adjacent to ∠b.

Explanation:

Step1: Recall right - triangle side definitions

In a right - triangle with respect to an acute angle, the hypotenuse is the side opposite the right - angle, the opposite side is the side not touching the angle, and the adjacent side is the non - hypotenuse side that touches the angle.
For right - triangle \(ABC\) with right - angle at \(C\) and considering \(\angle B\), the hypotenuse is \(\overline{AB}\) (the side opposite the right - angle \(\angle C\)). The side opposite \(\angle B\) is \(\overline{AC}\) (the side that does not touch \(\angle B\) among the non - hypotenuse sides), and the side adjacent to \(\angle B\) is \(\overline{BC}\) (the non - hypotenuse side that touches \(\angle B\)).

Step2: Evaluate students' statements

Tomas has the adjacent and opposite sides reversed with respect to \(\angle B\). Iliana correctly states that \(\overline{AB}\) is the hypotenuse, \(\overline{BC}\) is the opposite side to \(\angle B\), and \(\overline{AC}\) is the adjacent side to \(\angle B\).

Answer:

Iliana is correct; \(BC\) is opposite \(\angle B\) and \(AC\) is adjacent to \(\angle B\).