Final answer:
To find the distance between Eugene, OR and Chicago, IL using latitude and longitude coordinates, the latitudinal and longitudinal differences are multiplied by their respective conversion factors. The Pythagorean theorem gives us a distance of approximately 1942.72 miles, which does not match any of the provided options, indicating a possible error in the calculations or the question itself.
Step-by-step explanation:
The question involves determining the distance between two cities using latitude and longitude coordinates. The distance in terms of latitude is found by taking the difference in latitude degrees and multiplying by 69 miles per degree. Similarly, the longitude distance is calculated by taking the difference in longitude degrees and multiplying by 54.6 miles per degree. Finally, the Pythagorean theorem is used to find the straight-line distance.
- Latitude difference: |44.0521° N - 41.8781° N| = 2.174°
- Latitude distance: 2.174° * 69 mi/deg = 150.006 mi
- Longitude difference: |123.0868° W - 87.6298° W| = 35.457°
- Longitude distance: 35.457° * 54.6 mi/deg = 1937.95 mi
- Pythagorean theorem: √(150.006² + 1937.95²) = √3774171.8
- Total distance: √3774171.8 ≈ 1942.72 mi
After rounding to the nearest hundredth, the answer is 1942.72 mi. This does not match any of the provided options, so it's possible there's a miscalculation or typo in the original question or the conversion factors provided. For this reason, none of the answer choices A, B, C, or D are correct based on the calculations made with the provided information.