The branch of surveying in which both horizontal and vertical positions of a point, are determined by making instrumental observations, is known

ANS:D - all the above.

Tacheometry.

Tacheometry (or Tachemetry or Telemetry) is a branch of angular surveying in which the horizontal and vertical distances of points are obtained by optical means as opposed to the ordinary slower process of measurements by tape or chain. The method is very rapid and convenient. A tachymeter or tacheometer is a type of theodolite used for rapid measurements and determines, electronically or electro-optically, the distance to target. The principles of action are similar to those of rangefinders. I think the answer should be a) Tacheometry.

Is a system of rapid surveying, by which the horizontal and vertical positions of points on the earth's surface relative to one another are determined without using a chain or tape, or a separate levelling instrument.