A 7.5 minute quadrangle typically covers approximately how many square miles?

A 7.5 minute quadrangle typically covers approximately how many square miles?

• A. 49-70 square miles
• B. 20-30 square miles
• C. 80-100 square miles
• D. 100-120 square miles

Answer: (A)

A 7.5-minute quadrangle is the map area bounded by 7.5 minutes of latitude and 7.5 minutes of longitude, so its size comes from how far those minutes span on the Earth's surface. The north–south extent is fixed: 7.5 minutes of latitude is about 7.5 nautical miles, which is roughly 8.63 miles. The east–west extent depends on latitude because longitude distances shrink toward the poles; at a given latitude φ, 7.5 minutes of longitude covers about 7.5 nautical miles × cos φ, which converts to approximately 8.63 × cos φ miles. Therefore the area is roughly 8.63 miles × (8.63 × cos φ) ≈ 74.6 × cos φ square miles. At typical mid-latitudes in the continental United States, cos φ is around 0.7–0.9, giving an area near 50–70 square miles. That makes about 49–70 square miles a good approximation for a 7.5-minute quadrangle. The other ranges are off because they would imply much smaller or much larger extents than this standard rectangle defines.

A 7.5-minute quadrangle is the map area bounded by 7.5 minutes of latitude and 7.5 minutes of longitude, so its size comes from how far those minutes span on the Earth's surface. The north–south extent is fixed: 7.5 minutes of latitude is about 7.5 nautical miles, which is roughly 8.63 miles. The east–west extent depends on latitude because longitude distances shrink toward the poles; at a given latitude φ, 7.5 minutes of longitude covers about 7.5 nautical miles × cos φ, which converts to approximately 8.63 × cos φ miles. Therefore the area is roughly 8.63 miles × (8.63 × cos φ) ≈ 74.6 × cos φ square miles. At typical mid-latitudes in the continental United States, cos φ is around 0.7–0.9, giving an area near 50–70 square miles. That makes about 49–70 square miles a good approximation for a 7.5-minute quadrangle. The other ranges are off because they would imply much smaller or much larger extents than this standard rectangle defines.