1. **Problem statement:** An airplane flies on a course of S 300 E for 150 km. We need to find how far south the plane is from its starting point. 2. **Understanding the direction:** The course S 300 E means the plane is flying 30 degrees east of due south (since 300° from north clockwise is equivalent to 30° east of south). 3. **Formula used:** To find the southward displacement, we use the component of the distance along the south direction: $$\text{South distance} = 150 \times \cos(30^\circ)$$ 4. **Calculate cosine:** $$\cos(30^\circ) = \frac{\sqrt{3}}{2} \approx 0.866$$ 5. **Calculate south distance:** $$150 \times 0.866 = 129.9$$ 6. **Answer:** The plane is approximately 129.9 km south of its origin.