1. **Problem:** In triangle ABC, given angles $c=36^\circ$, $B=24^\circ$, and side $a$ unknown, find angles $A$, sides $b$, and $c$. 2. **Formula:** Use the triangle angle sum rule: $$A + B + C = 180^\circ$$ and the Law of Sines: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ 3. **Step 1:** Find angle $A$. $$A = 180^\circ - B - c = 180^\circ - 24^\circ - 36^\circ = 120^\circ$$ 4. **Step 2:** Use Law of Sines to find sides $b$ and $c$ in terms of $a$. $$\frac{a}{\sin 120^\circ} = \frac{b}{\sin 24^\circ} = \frac{c}{\sin 36^\circ}$$ 5. **Step 3:** Express $b$ and $c$: $$b = a \times \frac{\sin 24^\circ}{\sin 120^\circ}$$ $$c = a \times \frac{\sin 36^\circ}{\sin 120^\circ}$$ 6. **Explanation:** We found $A$ by subtracting known angles from 180°. Then, using the Law of Sines, we related sides to their opposite angles. Since $a$ is unknown, $b$ and $c$ are expressed relative to $a$. **Final answers:** $$A = 120^\circ$$ $$b = a \times \frac{\sin 24^\circ}{\sin 120^\circ}$$ $$c = a \times \frac{\sin 36^\circ}{\sin 120^\circ}$$