1. **Problem statement:** We need to find the length of the walking trail BC in triangle ABC where angle A = 54°, angle B = 65°, and side AC = 7 km. 2. **Formula and rules:** Use the Law of Sines which states: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ where $a$, $b$, and $c$ are sides opposite angles $A$, $B$, and $C$ respectively. 3. **Find angle C:** Since the sum of angles in a triangle is 180°, $$C = 180^\circ - A - B = 180^\circ - 54^\circ - 65^\circ = 61^\circ$$ 4. **Assign sides:** Side AC = 7 km is opposite angle B (65°), so $b = 7$ km. We want to find side BC, which is opposite angle A (54°), so $a = BC$. 5. **Apply Law of Sines:** $$\frac{a}{\sin 54^\circ} = \frac{7}{\sin 65^\circ}$$ 6. **Solve for $a$:** $$a = \frac{7 \times \sin 54^\circ}{\sin 65^\circ}$$ Calculate the sines: $$\sin 54^\circ \approx 0.8090, \quad \sin 65^\circ \approx 0.9063$$ 7. **Substitute values:** $$a = \frac{7 \times 0.8090}{0.9063} = \frac{5.663}{0.9063}$$ 8. **Simplify:** $$a \approx 6.25 \text{ km}$$ 9. **Answer:** The closest option is c. 6.1 km. Final answer: **6.1 km**