1. **State the problem:** 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:** Bearings are 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. **Break down the distance into components:** We can use trigonometry to find the south and west components of the ship's travel. The south component corresponds to the vertical (y) direction, and the west component corresponds to the horizontal (x) direction. 4. **Calculate the angle relative to the south direction:** Since 243.7 degrees is more than 180 degrees, the ship is in the southwest quadrant. The angle from the south direction is $$243.7^\circ - 180^\circ = 63.7^\circ$$. 5. **Formulas:** - South distance = $$200 \times \cos(63.7^\circ)$$ - West distance = $$200 \times \sin(63.7^\circ)$$ 6. **Calculate the south distance:** $$200 \times \cos(63.7^\circ) = 200 \times 0.447 = 89.4 \text{ km}$$ 7. **Calculate the west distance:** $$200 \times \sin(63.7^\circ) = 200 \times 0.894 = 178.8 \text{ km}$$ **Final answers:** - a) The ship has traveled approximately 89.4 km south. - b) The ship has traveled approximately 178.8 km west.