For first-order triangulation, the desirable limit of the strength of figure R between bases is which value?

For first-order triangulation, the desirable limit of the strength of figure R between bases is which value?

• A. 10
• B. 20
• C. 25
• D. 30

Answer: (B)

In a first-order triangulation, the strength of a figure tells us how well the geometry of a triangle will hold up against measurement errors; it’s a measure of how robust the figure is when bases and angles are used to compute coordinates. A desirable limit keeps the triangle well-conditioned: not too stretched or acute, so that errors in base measurements or angles don’t get amplified as the network is propagated. The value 20 is chosen as the practical upper limit for the strength of figure R between bases because it strikes a balance between being strict enough to avoid weak, error-prone geometry and being lenient enough to allow feasible measurement work. When the strength stays at or below this limit, the figures are typically robust enough to preserve the intended accuracy of a first-order network. If the limit were higher, there would be more rooms for slender or awkward figures that can magnify errors; if it were much lower, the surveying tasks would become overly restrictive and inefficient.

In a first-order triangulation, the strength of a figure tells us how well the geometry of a triangle will hold up against measurement errors; it’s a measure of how robust the figure is when bases and angles are used to compute coordinates. A desirable limit keeps the triangle well-conditioned: not too stretched or acute, so that errors in base measurements or angles don’t get amplified as the network is propagated.

The value 20 is chosen as the practical upper limit for the strength of figure R between bases because it strikes a balance between being strict enough to avoid weak, error-prone geometry and being lenient enough to allow feasible measurement work. When the strength stays at or below this limit, the figures are typically robust enough to preserve the intended accuracy of a first-order network. If the limit were higher, there would be more rooms for slender or awkward figures that can magnify errors; if it were much lower, the surveying tasks would become overly restrictive and inefficient.