Angles can be measured in degrees, minutes, seconds, or radians. Degrees are commonly used and there are conversion formulas between degrees and radians. Angles are used to describe direction and position in surveying, with common types including vertical, horizontal, deflection, and interior angles. Surveying directions make use of cardinal directions, meridians, magnetic declination, bearings, and azimuths to define lines and positions on the ground in reference to a coordinate system. True north is defined by the Earth's axis, while magnetic north varies over time.

1. Angles and Directions

2. Angle Units and Conversion/Equivalents
 Angles. Measured directly in the field by some device such as compass,
transit, theodolite, sextant or plane table and alidade.
 figure formed by diverging lines: a figure formed by two lines diverging
from a common point or two planes diverging from a common line.
 Units of Angles
 Degrees, Minutes and Seconds/sexagesimal units
 Radians. One radian is a measure of angle, which, if its vertex is
placed at the center of the circle, subtends on the circumference an
arc equal to the radius of the circle.
Radian = (Pi / 180o)
Degrees = (180o / Pi)
 Slope (%) slope Slope= rise x 100
rise run
run

3. Unit of Measurement
• Linear measurement – meter/kilometer
(ground); cm or mm (on paper)
• Angular measurement
I. Sexagesimal units – degree, minute and second
II. Centisimal unit – in decimal
• Area measurement: sq.cm(map); m, sq.m,
sq.km, ha. (ground)

4. Dist. Between Two points
• Formula
Distance = (Y2-Y1)2 + (X2-X1)2 )

5. Common Types of Angles

6. Vertical and Horizontal Angles
Vertical Angle. An angle between two
intersecting lines in vertical lines. Angles
opposite each other when two lines cross.
Deflection Angle
Interior Angle

7. Deflection Angle
 The angle between a line and the
prolongation of the preceding lines.

8. Interior Angle
Interior Angle (IA). The angles between
adjacent lines inside the figures of a closed
polygon.
Sum of IA = (n-2) × 180°
, where n = No. of corners

14. Surveying Directions
 Cardinal Directions: North, South, West, East
 Meridians. A fixed line of reference for determining direction. It is
a line to which the direction of all lines of a survey is referred.
 Magnetic Declination. That angle between the true meridian
and the magnetic meridian. It varies more or less systematically
over some period of time.
 Bearing. The direction of any lines with respect a given meridian.
The quadrant in which the line falls and the acute angle, which
the line makes with the meridian in that quadrant, indicate it.
 Azimuths. A line with its direction as given by the angle between
the meridian and the line, measured in a clockwise direction
usually from the south point of the meridian. The clockwise angle
designated of being measured either the north end or south end
of the reference meridian and the line in question.

15. Different Kinds of Meridians
• True Meridian. A true north and south lines
passing through the geographical poles of the
earth, and it is established by astronomical
observations. The direction from any point along
a meridian towards the North Pole of the earth is
defined as true north. That is, the north according
to the earth’s axis. True north is also known as
geographic north.
Magnetic Meridian.
• Assumed Meridian. If the meridian is arbitrarily
chosen.
• Grid Meridian.

16. Bearing
• BearingThe direction of any lines with respect
a given meridian. The quadrant in which the
line falls and the acute angle, which the line
makes with the meridian in that quadrant,
indicate it.

17. 2 kinds of Azimuth
 North Reckoned A.
South Reckoned A.

18. Solve:

19. The Coordinate System
Mathematical Coordinate
 X axis & Y axis
Geographic Coordinate
 Latitude & Longitude
Plane Coordinate: Universal Transverse
Mercator (UTM) Coordinate
 Northing & Easting
 Diff in N & E: Latitude & Departure

20. END…