Intervisibility across equal-elevation hilltops Two hilltops A and B are 20 km apart and an intervening top C lies between them. If the highest (top) contour of all three hilltops has the same elevation value, the straight line of sight AB will most likely:

Introduction / Context:
Intervisibility problems in surveying combine geometry of straight sight lines with the curved earth surface (and sometimes standard refraction). When two points at equal elevation are far apart, the straight chord joining them lies below the earth’s surface between the points. This affects whether an intervening hilltop of the same elevation will obstruct the view.

Given Data / Assumptions:

• A and B have equal elevation (same top contour value) and are 20 km apart.
• Hilltop C is between them and has the same top contour value as A and B.
• The line of sight is a straight line (light ray approximation without advanced refraction corrections).

Concept / Approach:

Between two points on a sphere at the same elevation, the straight line (chord) connecting them lies below the curved surface midway. Therefore, any point at the same elevation located between A and B will usually stand above the straight line of sight. Over 20 km, earth curvature drop is significant (approximate curvature drop h ≈ 0.067 * D^2 meters where D is distance in km). This drop makes the central terrain higher relative to the chord, causing obstruction if elevations are equal.

Step-by-Step Solution:

Verification / Alternative check:

Using the curvature drop estimate: for 20 km, h ≈ 0.067 * 20^2 ≈ 26.8 m (without refraction). Even with standard refraction partially offsetting curvature, the obstruction typically remains for equal elevations.

Why Other Options Are Wrong:

Passing clear or grazing would require C to be lower than the chord or just tangent; equal elevations make obstruction more likely. Curvature is not negligible at 20 km.

Common Pitfalls:

Assuming the line of sight follows ground curvature; it does not—it is straight (neglecting atmospheric refraction).

Final Answer:

Pass below the hilltop C (be obstructed at C)