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 a given non - right angle, the hypotenuse is the side opposite the right angle, the opposite side is the side that does not form the given angle, and the adjacent side is the non - hypotenuse side that forms the given angle.

Step2: Analyze with respect to ∠B

In right - triangle ABC with right angle at C, for ∠B, the side opposite the right angle is AB (so AB is the hypotenuse). The side that does not form ∠B is AC (so AC is the opposite side to ∠B), and the non - hypotenuse side that forms ∠B is BC (so BC is the adjacent side to ∠B).

Answer:

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