What is the method of establishing a geodetic control survey using connected triangles called?

The method of establishing a geodetic control survey using connected triangles is known as trilateration. This technique employs the measurement of distances between points, which allows for the creation of a network of triangles in the geodetic framework. By calculating these distances, surveyors can accurately determine the positions of various points based on their relationships to one another.

Trilateration relies on the principle that knowing the lengths of the sides of triangles permits the calculation of angles and, consequently, the locations of points in a coordinate system. This method is particularly useful in geodetic surveys because it provides high accuracy and reliability when establishing control points over large areas.

The other choices represent different aspects of surveying and geodesy but do not specifically refer to establishing control surveys through the method of connected triangles. Trigonometry is a broader mathematical discipline that deals with the relationships between angles and distances. A traverse refers to a series of connected survey lines, which may include horizontal and vertical angles, but it does not specifically denote the triangular connection method. Geodesy is the scientific discipline that encompasses both surveying techniques and the study of the Earth's geometric shape, orientation in space, and gravity field, but it is not a specific method for establishing control surveys.