Triangulation quality – well-conditioned triangle: In primary/secondary triangulation, a triangle is considered well conditioned if no angle is less than what minimum value?

Introduction / Context:
The accuracy of computed sides and angles in triangulation depends strongly on the geometry of the triangles observed. “Well-conditioned” triangles minimize propagation of observational errors. A common rule-of-thumb sets bounds on the smallest and largest permissible angles.

Given Data / Assumptions:

• Angle observations are affected by small systematic and random errors.
• Error magnification increases in very acute or very obtuse triangles.
• We target robust geometry rather than perfectly equilateral shapes.

Concept / Approach:
Classical practice recommends triangles with angles roughly between 30° and 120°. The lower bound of 30° avoids excessive sensitivity of computed lengths to small angle errors, while the upper bound follows from the angle sum of a triangle. Equilateral (60° each) is ideal, but rarely achievable in the field; ensuring no angle is less than 30° maintains good conditioning for network adjustment.

Step-by-Step Solution:

Verification / Alternative check:
Condition numbers and variance–covariance analysis of angle–side computations confirm that very acute angles yield large standard deviations in derived lengths.

Why Other Options Are Wrong:

• 20°: too acute, poor conditioning.
• 45° or 60°: desirable but unnecessarily strict; many workable triangles have smaller angles than these.

Common Pitfalls:
Accepting long skinny triangles for convenience; forgetting that angle misclosures increase with poor geometry; ignoring station intervisibility constraints that can be mitigated by alternate station placement.

Final Answer:
30°