Which of the following types of surveys utilizes a telescopic instrument?

In surveying, a telescopic instrument is most commonly associated with the stadia survey method. This technique employs a theodolite or transit equipped with a telescopic sight to measure distances based on the angles seen through the instrument. The stadia method utilizes a set of horizontal and vertical crosshairs to determine the distance to an object based on the top and bottom readings of the staff held at that point, applying specific formulas based on the angle of elevation or depression.

Plane table surveys, on the other hand, do not typically employ telescopic instruments; instead, they use a plane table along with alidade for direct line of sight measurement and sketching of the survey area. Zoned surveys, while focused on dividing land into manageable areas, do not necessarily entail the use of telescopic instruments, leaning more towards administrative or planning techniques. Triangulation involves calculating distances by forming triangles between points; typically, it relies on theodolites that can have telescopic features, but is not exclusively defined by their use.

Thus, the stadia survey stands out as the method that specifically uses a telescopic instrument to measure distances and angles directly, making it the correct choice in this context.