GEFS-CE11 - (FUNDAMENTALS OF SURVEYING)
ENGR. MMMayos UNIVERSITY OF THE CORDILLERAS MODULE 2
MEASUREMENT OF DIRECTIONS, BEARINGS AND ANGLES
Note:
Supplement this lecture note by reading part V (measurement of angles and
directions) of the book of La Putt, J.P., Elementary Surveying and Chapter 12
(angles and directions) of the book of Foote, et.al., Surveying.
Location of a point
The location of a point is fixed if measurements are made of (a) its direction and distance
from a known point, (b) its direction from two known points, (c) its distance from two
points, or (d) its direction from one known point and its distance from another.
Direction of a line
For horizontal projection or plan, the direction of any line is defined by the horizontal angle
between the line and some reference line (meridian) and for vertical projection, the
direction of one point with respect to another is defined by the vertical angle between the
plane of the horizon and the line joining the two points. In surveying practice directions
may be defined by means of: bearings, azimuths, deflection angles, interior angles, and
angles to the right.
True meridian – a line passing through the geographic north and south poles of
the earth and the observer’s position.
Bearings
The bearing of a line is the acute horizontal angle (00 to 900) between the reference
meridian and the line. If the acute angle is equal to 00, the bearing is either read as due
north or due south and if the acute angle is equal to 900, the bearing is either read as due
east or due west. A quadrantal system is used to specify bearings such that a line may
fall under one of the following quadrants: NE, SE, NW, and SW. each quadrant is
numbered from 0 to 90 degrees from either north or south end of the meridian to the east
or west end of the reference parallel
N
00
REFERENCE MERIDIAN (N – S line)
NORTH – WEST (NW) NORTH – EAST (NE)
QUADRANT QUADRANT
E
90 W
0 0
90
REFERENCE PARALLEL (E – W line)
SOUTH – WEST (SW) SOUTH – EAST (SE)
QUADRANT QUADRANT
0
0
S
, GEFS-CE11 - (FUNDAMENTALS OF SURVEYING)
ENGR. MMMayos UNIVERSITY OF THE CORDILLERAS MODULE 2
N
α
β
W E
θ
ø
S
Bearing description for different directions
Azimuths
The azimuth of a line is its direction as given by the angle between the meridian and the
line measured in a clockwise direction from either the north or south branch of the
meridian. The azimuth of a line may range from 00 to 3600 and letters are not required to
identify quadrants.
N
W E
α
θ
ø
β S
Azimuth description for different directions
ENGR. MMMayos UNIVERSITY OF THE CORDILLERAS MODULE 2
MEASUREMENT OF DIRECTIONS, BEARINGS AND ANGLES
Note:
Supplement this lecture note by reading part V (measurement of angles and
directions) of the book of La Putt, J.P., Elementary Surveying and Chapter 12
(angles and directions) of the book of Foote, et.al., Surveying.
Location of a point
The location of a point is fixed if measurements are made of (a) its direction and distance
from a known point, (b) its direction from two known points, (c) its distance from two
points, or (d) its direction from one known point and its distance from another.
Direction of a line
For horizontal projection or plan, the direction of any line is defined by the horizontal angle
between the line and some reference line (meridian) and for vertical projection, the
direction of one point with respect to another is defined by the vertical angle between the
plane of the horizon and the line joining the two points. In surveying practice directions
may be defined by means of: bearings, azimuths, deflection angles, interior angles, and
angles to the right.
True meridian – a line passing through the geographic north and south poles of
the earth and the observer’s position.
Bearings
The bearing of a line is the acute horizontal angle (00 to 900) between the reference
meridian and the line. If the acute angle is equal to 00, the bearing is either read as due
north or due south and if the acute angle is equal to 900, the bearing is either read as due
east or due west. A quadrantal system is used to specify bearings such that a line may
fall under one of the following quadrants: NE, SE, NW, and SW. each quadrant is
numbered from 0 to 90 degrees from either north or south end of the meridian to the east
or west end of the reference parallel
N
00
REFERENCE MERIDIAN (N – S line)
NORTH – WEST (NW) NORTH – EAST (NE)
QUADRANT QUADRANT
E
90 W
0 0
90
REFERENCE PARALLEL (E – W line)
SOUTH – WEST (SW) SOUTH – EAST (SE)
QUADRANT QUADRANT
0
0
S
, GEFS-CE11 - (FUNDAMENTALS OF SURVEYING)
ENGR. MMMayos UNIVERSITY OF THE CORDILLERAS MODULE 2
N
α
β
W E
θ
ø
S
Bearing description for different directions
Azimuths
The azimuth of a line is its direction as given by the angle between the meridian and the
line measured in a clockwise direction from either the north or south branch of the
meridian. The azimuth of a line may range from 00 to 3600 and letters are not required to
identify quadrants.
N
W E
α
θ
ø
β S
Azimuth description for different directions
