1. **State the problem:** Town A is 30 km north of town B. A ship sails 25 km from town A on a bearing of 120°. We need to find how far east and south the ship is from town B. 2. **Understanding bearings:** A bearing of 120° means the direction is measured clockwise from north. So, 120° is 30° east of due south (since 120° - 90° = 30°). 3. **Set up coordinate system:** Let town B be at the origin $(0,0)$. Since town A is 30 km north of B, town A is at $(0,30)$. 4. **Calculate ship's displacement from A:** The ship sails 25 km at 120° bearing from A. - The angle from the positive x-axis (east) is $90° + 30° = 120°$. - The east (x) component of the ship's displacement from A is: $$x = 25 \times \sin(120^\circ) = 25 \times \frac{\sqrt{3}}{2} = 21.65 \text{ km}$$ - The north (y) component of the ship's displacement from A is: $$y = 25 \times \cos(120^\circ) = 25 \times (-\frac{1}{2}) = -12.5 \text{ km}$$ 5. **Find ship's coordinates relative to B:** - East coordinate from B: $0 + 21.65 = 21.65$ km east - North coordinate from B: $30 + (-12.5) = 17.5$ km north 6. **Find how far east and south the ship is from B:** - East distance is $21.65$ km. - Since the ship is still north of B by 17.5 km, the south distance from B is $0$ km. **Final answer:** The ship is approximately 21.65 km east and 0 km south of town B.