Meridians on a sphere — distance between longitudes at higher latitudes If the separation between two meridians measured along the equator is 100 km, what will be the horizontal distance between the same two meridians measured along the parallel of latitude 60° (assume a spherical Earth so that spacing scales with cos(latitude))?

Introduction / Context:
In geodesy and plane surveying, distances between meridians (lines of longitude) vary with latitude. Along the equator, meridians are farthest apart; toward the poles they converge. This question tests the fundamental cosine scaling that converts an equatorial spacing to the spacing along any parallel (line of latitude).

Given Data / Assumptions:

• Equatorial distance between two meridians = 100 km.
• Required distance is along the parallel of latitude 60°.
• Idealized spherical Earth and small-arc approximation so linear scaling by cos(latitude) applies.

Concept / Approach:
At latitude φ, the radius of the parallel equals Earth radius * cos φ. Hence any arc length between the same longitudes at latitude φ equals the corresponding equatorial arc multiplied by cos φ. Therefore, distance at latitude φ = (equatorial distance) * cos φ.

Step-by-Step Solution:

Verification / Alternative check:
At 0° (equator), cos 0° = 1, so spacing is unchanged; at 90° (pole), cos 90° = 0, so meridians meet (distance becomes 0). The computed 50 km at 60° matches this trend.

Why Other Options Are Wrong:

• 100 km and higher values ignore the cosine reduction with latitude.
• 150 km, 400 km, 500 km would imply spacing grows toward the pole, which is physically impossible.

Common Pitfalls:
Confusing the longitude degree-length (which varies with latitude) with the latitude degree-length (nearly constant); forgetting to multiply by cos φ when converting equatorial spacing to spacing on a parallel.

Final Answer:
50 km