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A horizontal angle is measured in a plane that is horizontal at the point of
measurement. When horizontal angle is measured between points, which do not lie
directly in the plane, it is measured between the perpendiculars extended to the
plane from those points.
A vertical angle is measured in a plane that is vertical at the point of
observation or measurement. Horizontal and vertical angles are measured with an
instrument called a transit or theodolite.

1.3 Types of Surveying
There are two types of surveying: these are
1. Plane surveying
As mentioned earlier that most surveying measurements are carried out as if
the surface of the earth were perfectly flat. The method of surveying based on this
assumption is called plane surveying. In plane surveying, it is neglect the curvature
of the earth, and it is used the principles of plane geometry and plane trigonometry
to compute the result of our surveys.
The use of plane surveying methods simplifies the work of surveyor. Within a
distance of 20 km, the effect of earth’s curvature on our measurement is so small
that we can hardly measure it. In other words, a horizontal distance measured
between two points along a truly level line is, for practical purposes, the same
distances measured along the straight chord connecting the two points.
In plane surveying horizontal lines are assumed to be straight line and all
vertical lines are parallel.

Fig. 1.4. In plane surveying, the curvature of the earth is neglected, and vertical distances
are measured with reference of a flat plane

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