1. **State the problem:** We have a triangle ABC with side AC = 3, angle A = 35°, and angle C = 85°. We need to find the length of side BC, denoted as $x$. 2. **Use the Law of Sines:** The Law of Sines states that in any triangle, $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $a$, $b$, and $c$ are sides opposite angles $A$, $B$, and $C$ respectively. 3. **Find angle B:** Since the sum of angles in a triangle is 180°, $$B = 180^\circ - A - C = 180^\circ - 35^\circ - 85^\circ = 60^\circ$$ 4. **Assign sides:** Side AC = 3 is opposite angle B (since AC is between A and C, side BC is opposite A, side AB is opposite C). But from the description, side AC = 3 is opposite angle B = 60°. 5. **Apply Law of Sines to find $x = BC$ (opposite angle A = 35°):** $$\frac{AC}{\sin B} = \frac{BC}{\sin A} \Rightarrow \frac{3}{\sin 60^\circ} = \frac{x}{\sin 35^\circ}$$ 6. **Solve for $x$:** $$x = \frac{3 \times \sin 35^\circ}{\sin 60^\circ}$$ 7. **Calculate values:** $$\sin 35^\circ \approx 0.574 \quad \text{and} \quad \sin 60^\circ \approx 0.866$$ 8. **Compute $x$:** $$x \approx \frac{3 \times 0.574}{0.866} = \frac{1.722}{0.866} \approx 1.988$$ **Final answer:** $$x \approx 1.99$$ The length of side BC is approximately 1.99 units.