1. **Stating the problem:** We have a right triangle \(\triangle ABC\) inscribed in a circle where \(CA\) is the diameter. We need to identify the hypotenuse, adjacent, and opposite sides relative to angle \(\theta\) at vertex \(C\). 2. **Important rule:** In a right triangle, the hypotenuse is the side opposite the right angle and is the longest side. The adjacent side is the side next to the angle of interest (other than the hypotenuse), and the opposite side is the side opposite the angle of interest. 3. **Answering each part:** - a) The diameter \(CA\) is the hypotenuse of \(\triangle ABC\) because it is opposite the right angle at \(B\). - b) Side \(BC\) is opposite angle \(\theta\), so it is the opposite side. - c) Side \(AB\) is adjacent to angle \(\theta\) (it shares vertex \(B\) with \(C\) and is not the hypotenuse), so it is the adjacent side. **Final answers:** - a) hypotenuse - b) opposite - c) adjacent