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 the bearing:** 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:** 243.7 degrees is in the third quadrant (between 180 and 270 degrees), so the ship is moving southwest. 4. **Formulas used:** To find the south and west components of the distance traveled, we use trigonometry: - South distance = $200 \times \cos(243.7^\circ - 180^\circ) = 200 \times \cos(63.7^\circ)$ - West distance = $200 \times \sin(243.7^\circ - 180^\circ) = 200 \times \sin(63.7^\circ)$ 5. **Calculations:** - Calculate $\cos(63.7^\circ)$ and $\sin(63.7^\circ)$: - $\cos(63.7^\circ) \approx 0.4472$ - $\sin(63.7^\circ) \approx 0.8944$ - South distance = $200 \times 0.4472 = 89.44$ km - West distance = $200 \times 0.8944 = 178.88$ km 6. **Interpretation:** The ship has traveled approximately 89.44 km south and 178.88 km west. **Final answers:** - a) South distance = 89.44 km - b) West distance = 178.88 km