1. **Problem statement:** A plane travels 200 miles at a heading of 300° from an airport. We need to find how far west of the airport the plane is. 2. **Understanding headings:** Headings are measured clockwise from north (0°). East is 90°, south is 180°, west is 270°, and 300° is between west (270°) and north (0°). 3. **Formula:** The westward distance is the horizontal component of the displacement vector. We use the cosine function because cosine gives the adjacent side (horizontal) in a right triangle: $$\text{West distance} = 200 \times \cos(\theta)$$ where $\theta$ is the angle from the east-west axis. Since 300° is measured from north, the angle from the west direction (270°) is $300° - 270° = 30°$. 4. **Calculate west distance:** $$\text{West distance} = 200 \times \cos(30°)$$ 5. **Evaluate cosine:** $$\cos(30°) = \frac{\sqrt{3}}{2} \approx 0.866$$ 6. **Multiply:** $$200 \times 0.866 = 173.2$$ 7. **Interpretation:** The plane is approximately 173.2 miles west of the airport. **Final answer:** $$\boxed{173.2 \text{ miles west}}$$