Question

Which of the following triangles are well conditioned and may be suitable for control establishment using triangulation? 

• A. I
• B. II
• C. III
• D. IV

Hint:

For triangulation, try to keep all angles between $30^\circ$ and $120^\circ$ (ideally near $60^\circ$) to minimize propagation of angular errors into side lengths.

Answer 1

The Correct Option is A

A well-conditioned triangulation triangle avoids very small or very large angles; in practice, angles are usually kept within about \(30^\circ\) and \(120^\circ\) (best near \(60^\circ\)). \[ \begin{aligned} \text{I: } & 45^\circ, 45^\circ, 90^\circ \in [30^\circ, 120^\circ] \Rightarrow \text{good}. \\ \text{II: } & 25^\circ, 25^\circ, 130^\circ \ (\text{one } <30^\circ, \ \text{one } >120^\circ) \Rightarrow \text{poor}. \\ \text{III: } & 35^\circ, 35^\circ, 110^\circ \in [30^\circ, 120^\circ] \Rightarrow \text{good}. \\ \text{IV: } & 25^\circ \ (<30^\circ) \Rightarrow \text{poor}. \end{aligned} \] Hence, triangles I and III are suitable.