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:

Step1: Recall right - triangle side definitions

In a right - triangle with respect to an acute angle, the hypotenuse is the longest side (opposite the right - angle). The opposite side is the side that does not form the acute angle and the adjacent side is the non - hypotenuse side that forms the acute angle.
In right - triangle $ABC$ with right - angle at $C$, for $\angle B$, the hypotenuse is $\overline{AB}$ (opposite the right - angle $\angle C$). The side opposite $\angle B$ is the side that does not form $\angle B$, which is $\overline{AC}$. The side adjacent to $\angle B$ is the non - hypotenuse side that forms $\angle B$, which is $\overline{BC}$.

Answer:

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