Which surveying method integrates theodolites with electronic distancing measurement?

The method that integrates theodolites with electronic distance measurement is Total Station Surveys. A Total Station is an advanced surveying instrument that combines a theodolite for measuring angles and an electronic distance measuring device (EDM) for determining distances, allowing for precise measurements of both horizontal and vertical angles, as well as distance in a single, efficient process. This integration enhances the speed and accuracy of surveying tasks, making it a common choice for land surveying, construction, and civil engineering projects.

In contrast, the other methods mentioned do not utilize this combination. Plane surveys focus solely on two-dimensional mapping or layout without the electronic components. Stadia surveys use a different technique based on the principle of a level staff and a telescope but do not incorporate electronic measurement technology. Photogrammetric surveys are based on taking photographs and extracting measurements from them rather than using a theodolite or EDM. Therefore, the unique functionalities of Total Station Surveys make them the correct answer in this context.