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 to ∠b. neither is correct because neither ac nor bc is opposite ∠b.

Explanation:

In right triangle \(ABC\) with right angle at \(C\), \(AB\) is the hypotenuse. For \(\angle B\), the opposite side is the one not connected to \(B\) (i.e., \(AC\)), and the adjacent side (non-hypotenuse) is the side forming \(\angle B\) (i.e., \(BC\)). Tomas correctly identifies these.

Answer:

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