A theodolite is a surveying instrument used for measuring horizontal and vertical angles. To measure long distances we use a system known as triangulation we can use, it, for instance, if we want to know the distance to the moon. Astronomers measure the angle of the moon above the horizon at two places on the earth’s surface as far apart as possible and at the same moment. This gives them a triangle and a base line (the distance between the two observations).
Since they have measured two angles of the triangle, they known the third, because the three angles of a triangle always add up to 1800. They therefore have enough information to find the distance between the apex (moon) and base line(earth). The same system is used in surveying and map making, but the surveyor’s base line is, of course, much shorter; in fact, both ends of the base line must be within sight of one another and of the next point to be observed. The theodolite is the basic instrument used in surveying, especially in precise triangulation.