1. **Problem statement:** A ship sails 200 km on a bearing of 243.7 degrees. We need to find how far south and how far west the ship has traveled. 2. **Understanding bearings:** A bearing is measured clockwise from the north direction. A bearing of 243.7 degrees means the ship is sailing in a direction 243.7 degrees clockwise from north. 3. **Breaking down the bearing:** Since 243.7 degrees is between 180 and 270 degrees, the ship is moving in the southwest quadrant. 4. **Using trigonometry:** To find the south and west components, we use sine and cosine functions relative to the angle from the south or west axis. 5. **Calculate the angle from the south direction:** The south direction is at 180 degrees, so the angle from south is $$243.7^\circ - 180^\circ = 63.7^\circ$$. 6. **Southward distance:** The southward component is the adjacent side to this angle, so $$\text{South} = 200 \times \cos(63.7^\circ)$$ 7. **Westward distance:** The westward component is the opposite side to this angle, so $$\text{West} = 200 \times \sin(63.7^\circ)$$ 8. **Calculate values:** $$\cos(63.7^\circ) \approx 0.445$$ $$\sin(63.7^\circ) \approx 0.896$$ 9. **Final distances:** $$\text{South} = 200 \times 0.445 = 89 \text{ km}$$ $$\text{West} = 200 \times 0.896 = 179.2 \text{ km}$$ **Answer:** (a) The ship has traveled approximately 89 km south. (b) The ship has traveled approximately 179.2 km west.