Small-angle facts and error growth in traverses: Which of the following statements are correct regarding angular/linear relations and error propagation?

Introduction / Context:Survey accuracy depends on both angular and linear measurements. Small-angle approximations and empirical error growth rules guide specifications, checking, and adjustment strategies in traversing and triangulation.

Given Data / Assumptions:

• Using standard small-angle relations in radians.
• Random errors assumed independent and unbiased.
• Practical field conditions with conventional instruments.

Concept / Approach:One radian equals about 57.3 degrees, hence 1 degree corresponds to ~1/57 rad. One arc-second equals about 1/206,265 rad, giving the 1:206,300 displacement ratio for small deflections. Random angular misclosures grow with sqrt(n) where n is the number of stations, while linear random errors tend to scale with total length measured, reflecting accumulation of many small unbiased contributions.

Step-by-Step Solution:

Verification / Alternative check:Bowditch (compass) rule and least-squares theory corroborate sqrt(n) angular propagation and length-proportional linear behavior in typical field work.

Why Other Options Are Wrong:Any single statement alone is incomplete; the bundle of all four best represents accepted surveying practice.

Common Pitfalls:Confusing systematic scale errors with random errors; mixing degree–radian conversions.

Final Answer:All of the above