two students describe the sides of right triangle abc in relation to ∠b. tomas: ab is the hypotenuse. ac is…
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.
Answer
Answer:
A. Tomas is correct; $\overline{AC}$ is opposite $\angle B$ and $\overline{BC}$ is adjacent to $\angle B$.
Explanation:
Step1: Recall trig - side definitions
In a right - triangle, for an angle $\theta$, the side opposite $\theta$ is the non - hypotenuse side that does not form $\theta$, and the adjacent side is the non - hypotenuse side that forms $\theta$.
Step2: Analyze with respect to $\angle B$
In right - triangle $ABC$ with right angle at $C$, for $\angle B$, the side opposite $\angle B$ is $\overline{AC}$ (it does not form $\angle B$) and the side adjacent to $\angle B$ is $\overline{BC}$ (it forms $\angle B$ along with the hypotenuse $\overline{AB}$). So Tomas is correct.