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Which of the following principle say this : “In isosceles triangle ratio to the perpendicular to the base is constant”
Surveying
Plan table
Tacheometry
All of these
Tacheometry
The basic principle of tacheometry is based on the property of isosceles triangles, where the ratio of the distance from the vertex to the base (perpendicular/height) to the length of the base (intercept) remains constant. In tacheometric surveying, the distance is measured indirectly by observing the staff intercept using a tacheometer equipped with stadia hairs.
The basic principle of tacheometry is based on the property of isosceles triangles, where the ratio of the distance from the vertex to the base (perpendicular/height) to the length of the base (intercept) remains constant. In tacheometric surveying, the distance is measured indirectly by observing the staff intercept using a tacheometer equipped with stadia hairs.
D=k⋅s+c — Distance equation in tacheometry
k=if=100 — Multiplying constant (ratio of focal length to stadia interval)
c=f+d=0 — Additive constant (for telescope fitted with anallatic lens)
In a tacheometer, the rays of light passing through the object glass form an isosceles triangle whose apex is at the optical center (or anallatic center). The distance D from the instrument station to the staff station is given by the relation D=k⋅s+c, where k is the multiplying constant (f/i) and c is the additive constant (f+d). For an anallatic lens, c=0, making distance directly proportional to the staff intercept s.
Tacheometry is an indirect method of surveying used to determine horizontal distances and elevations without chaining.
It relies on similar isosceles triangles where the ratio of perpendicular distance (D) to the staff intercept (s) is constant (k).
For an anallatic telescope, the additive constant c is eliminated (made zero), simplifying the distance formula to D=k⋅s.
Rapid surveying method suitable for steep, rough, or inaccessible terrains.
Eliminates the need for tedious manual chaining or taping.
Lower precision compared to direct chaining or modern Electronic Distance Measurement (EDM).
Accuracy heavily depends on clear visibility of the staff.
Preparation of contour maps and topographic surveys.
Location surveys for roads, railways, and reservoirs in hilly regions.
Option A (Surveying) is the general discipline of measuring positions on Earth; it encompasses multiple principles.
Option B (Plane Table) relies on graphical principles (e.g., intersection, resection, radiation) rather than stadia hair geometry.
C is correct — Tacheometry works on the geometric principle that in similar isosceles triangles, the ratio of the height (perpendicular distance to the staff) to the base (staff intercept) is constant.
Remember for competitive exams: Multiplying constant k=if is usually kept at 100, and additive constant c=f+d is kept at 0 using an anallatic lens.