Which survey method involves measuring the lengths of the triangle sides to define points?

The method that involves measuring the lengths of the triangle sides to define points is trilateration. This surveying technique is primarily based on the concept of determining the locations of points in a plane or space by measuring distances to them from known points. By measuring the lengths of the sides of triangles formed with known points, you can calculate the position of unknown points based on the geometric relationships of the triangles.

Trilateration is instrumental in many applications, including GPS technology, where distances from multiple satellites are used to pinpoint a location on Earth. The accuracy of this method comes from the mathematical principles that govern triangles, allowing surveyors to derive precise coordinates from distance measurements alone.

In contrast to other methods listed, such as photogrammetric surveys— which rely on photographs and visual data processing— or stadia surveys that utilize angular measurements to determine distance indirectly, trilateration is explicitly focused on direct distance measurements. Geodetic surveys involve more comprehensive considerations of large land areas and can include altitude measurements and the curvature of the Earth, distinguishing them from the more localized focus of trilateration.