Hydrographic surveying: In locating soundings by the method of two angles from the shore, how many range lines are required to be established?

Introduction:
Hydrographic surveys position depth soundings using various methods: intersecting ranges, sextant angles, or shore-based theodolite fixes. The method of two angles from the shore fixes the boat's position by observing two angles at known shore stations, avoiding the need for physical range markers.

Given Data / Assumptions:

• Two shore stations are established with known positions.
• Angles subtended by selected shore marks are measured from these stations to the boat.
• The objective is to locate the boat (sounding point) by resection/intersection.

Concept / Approach:
With two observed angles from known points, the boat's position is determined by the intersection of angle loci (arc/line constructs on the chart), not by aligning with pre-set ranges. Range lines are used in the "range method," where the boat keeps alignment with signals; here, angle observations replace them.

Step-by-Step Solution:
Set up two known shore stations and identify shore marks.Measure two angles to the boat position (or between marks) from these stations.Plot angle loci on the chart; their intersection fixes the boat's coordinates.Since angles suffice, no physical range line is necessary.

Verification / Alternative check:
Manuals distinguish range (transit) methods from angular fixes. The two-angle method is essentially resection and does not require range beacons.

Why Other Options Are Wrong:
Single or perpendicular range lines: These are range methods, not angle-based fixes.Three range lines: Overkill and not the described method.

Common Pitfalls:
Confusing different hydrographic positioning methods; assuming every method needs range beacons.

Final Answer:
No range line.