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, for an acute angle $\angle B$, the hypotenuse is the side opposite the right - angle. Here, in right - triangle $ABC$ with right - angle at $C$, $\overline{AB}$ is the hypotenuse. The opposite side to $\angle B$ is the side that does not form $\angle B$ and is not the hypotenuse, so $\overline{AC}$ is the opposite side to $\angle B$. The adjacent side to $\angle B$ is the non - hypotenuse side that forms $\angle B$, so $\overline{BC}$ is the adjacent side to $\angle B$.

Answer:

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