City A is at latitude 12° N and longitude 80° E. City B is at the same latitude 12° N but longitude 88° E. Using Earth's radius 6371 km, calculate the approximate distance between the two cities along the parallel.
Answer
≈870 km
The correct answer is ≈870 km — 6) The distance between City A and City B along the parallel is about 870 km.
Step-by-step solution
- 1) Find the difference in longitude: 88° E − 80° E = 8°. 2) Convert this difference to radians: 8° × π/180 ≈ 0.1396 rad. 3) Compute cos φ for φ = 12°: cos 12° ≈ 0.9781. 4) Use the formula for a parallel: d = R cos φ Δλ. 5) d = 6371 × 0.9781 × 0.1396 ≈ 870 km.
- 6) The distance between City A and City B along the parallel is about 870 km.
Common mistake: Forgetting to convert degrees to radians or omitting cos φ
Concept tested: Distance along a parallel using latitude and longitude
Published · How this solution was prepared and checked
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