1. **State the problem:** We need to find the length of side AC in the triangle formed by the lighthouse, boat A, and boat B. 2. **Given information:** - Height of lighthouse (vertical side) = 48 m - Distance from boat B to lighthouse base (horizontal side) = 187 m - Angle at boat A = 10° - Angle at boat B = $\theta = 14.4^\circ$ (from previous calculation) 3. **Find side AC:** Side AC is the distance between boats A and C (the base of the lighthouse). 4. **Use the fact that the total horizontal distance from A to B is 187 m + AC.** 5. **Use the tangent function at boat A:** $$\tan(10^\circ) = \frac{48}{AC}$$ 6. **Solve for AC:** $$AC = \frac{48}{\tan(10^\circ)}$$ 7. **Calculate:** $$\tan(10^\circ) \approx 0.1763$$ $$AC = \frac{48}{0.1763} \approx 272.3\text{ m}$$ **Final answer:** The length of side AC is approximately $272.3$ meters, correct to one decimal place.