What method is used when the distance between two points exceeds the maximum length of sight or the instrument cannot be set up between the points?

The method that is used when the distance between two points exceeds the maximum length of sight or when the instrument cannot be set up between the points is reciprocal leveling. This technique allows surveyors to determine height differences between two points that are far apart by taking measurements from both points separately and then adjusting for atmospheric conditions.

In reciprocal leveling, the surveyor sets up the leveling instrument at one point and takes a reading on a target at the opposite point. Then, the instrument is moved to the opposite point, and a corresponding reading is taken back on the first point. By comparing these readings, the surveyor can derive the difference in elevation between the two points while mitigating errors due to atmospheric refraction and other conditions. This method is particularly useful in situations where setting up an instrument directly between the two points is impractical.

In contrast, the other methods listed involve different approaches to surveying. Triangulation uses a network of triangles to measure distances and angles, which might be effective for long distances but doesn’t address the direct problem of instrument setup between two far points. Horizontal control is a method that pertains more to establishing precise horizontal positions rather than elevation differences, and terrain averaging deals with averaging measurements over uneven terrain but not specifically addressing the limitations posed by distance