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Which of the following is called a well-conditioned triangle?
< 30° and > 120°
30° and < 120°
20° and < 120°
< 20° and > 120°
30° and < 120°
A well-conditioned triangle in surveying is one where the angles are between 30° and 120°, ensuring that errors in measurement have the least impact on the plotted position of points. Triangles with angles outside this range are considered 'ill-conditioned' as they lead to significant plotting errors.
A well-conditioned triangle in surveying is one where the angles are between 30° and 120°, ensuring that errors in measurement have the least impact on the plotted position of points. Triangles with angles outside this range are considered 'ill-conditioned' as they lead to significant plotting errors.
30°<θ<120° — Criterion for a well-conditioned triangle
In chain surveying, the accuracy of a point's location depends on the intersection of two arcs. If an angle is very small (< 30°) or very large (> 120°), the intersection point of the arcs becomes 'fuzzy' or poorly defined due to the sharpness of the intersection, magnifying errors in chain measurements.
Well-conditioned triangles minimize errors in triangulation.
Ill-conditioned triangles occur when angles are < 30° or > 120°.
The best triangle is an equilateral triangle (60° each).
Small errors in chain length measurement propagate significantly in ill-conditioned triangles.
Reduces graphical plotting errors
Provides reliable control points for detail mapping
May require more base lines if terrain is complex
Can be difficult to maintain in constrained urban areas
Triangulation in chain surveying
Establishment of framework for large scale mapping
The concept is critical for ensuring the geometric stability of the survey framework.
If a triangle has an angle of 20°, it is considered ill-conditioned because the intersection point is too acute.
B is correct — A well-conditioned triangle is defined by angles ranging between 30° and 120°, which provides the best precision for plotting.
Always remember that 30° is the lower bound and 120° is the upper bound; mnemonically think of it as 30-120 range.