4.2: Reference Direction for Vertical Angles:

-Vertical angles: angle which used in slope distance corrections or in height determination

-Vertical angle are referenced to the:

(1) the horizon by plus (up) or minus (down) angles.

(2) zenith.

(3) nadir.

- Zenith and nadir are terms describing points on a celestial sphere .

4.3: Meridians:

- Meridians: a line on the mean surface of the earth joining the north and south poles.

- geographic meridian: is the line formed by the intersection with the earth’s surface of a plane that includes the earth’s axis of rotation.

- Magnetic meridians: are parallel to the directions taken by freely moving magnetized needles, as in a compass.

- Grid meridians: are lines that are parallel to a grid reference meridian (central meridian).

4.4: Horizontal Angles:

- Horizontal angles are usually measured with a theodolite or total station.

- For all closed polygons of n sides, the sum of the interior angles equal to (n-2)180 ْ .

- For all closed polygons of n sides, the sum of the exterior angles equal to (n+2)180 ْ .

Example: What is the sum of the interior angles for a five-sides polygon?

(5-2)180 ْ =

(3)(180) = 540 ْ

4.5: Azimuths:

- Azimuth: is the direction of a line as given by an angle measured clockwise (usually) from the north end of a meridian.

- Azimuths range in magnitude from 0 ْ to 360 ْ .

LineAzimuth

0-152 ْ

0-2121ْ

0-3202ْ

0-4325ْ

4.6: Bearings:

- Bearing: is the direction of a line as given by the acute angle between the line and a meridian.

- Measured clockwise or counterclockwise from the north or south end of the meridian.

- Bearing is always accompanied by letters that locate the quadrant in which the line falls (NE, NW, SE, or SW).

LineBearing

0-1N58ْ 00’E 0-2S25ْ 00’E 0-3S28ْ 00’W 0-4N10ْ 00’W

4.7: Relationships Between Bearings and Azimuths:

• To convert from azimuths to bearings by using this table:

quadrantquadrant lettersNumerical value

From 0 ْ to 90 ْNEbearing = azimuth

From 90 ْ to 180 ْSEbearing= 180 ْ - azimuth

From 180 ْ to 270 ْSWbearing= azimuth – 180 ْ

From 270 ْ to 360 ْNWbearing= 360 ْ - azimuth

• To convert from bearings to azimuths by using this relationships:

1. NE quadrant azimuth = bearing

2. SE quadrant azimuth = 180 – ْ bearing

3. SW quadrant azimuth = 180 – ْ bearing

4. NW quadrant azimuth = 360 – ْ bearing

• Example: convert :

1. 200 ْ 58’ = S20 ْ 58’W

2. N2 ْ 21’W = 357 ْ 39’

4.8: Reverse Directions:

• It can be said that every line has two direction.

• Forward direction is direction that oriented in the direction of fieldwork or computation staging.

• Back direction is direction that oriented in the reverse of the direction fieldwork or computation staging.

LineBearing

ABN 60 ْ 00’ E

BAS 60 ْ 00’ W

• To reverse a bearing … Reverse the direction letters.

Example:

• To reverse an azimuth …. Add 180 ْ to the original direction.

Example:

LineAzimuth

AB128 ْ 00’

BA308 ْ 00’

4.9: Azimuth Computations:

Az AB = 330 ْ 00’ (Given)

- 180 ْ

Az BA = 150 ْ 00’

+<B 120 ْ 28’

Az BC = 270 ْ 28’

START

Az BC = 270 ْ 28’

- 180 ْ

Az CB = 90 ْ 28’

+<C = 118 ْ 37’

Az CD = 209 ْ 05’

Az CD = 209 ْ 05’

- 180 ْ

Az DC = 29 ْ 05’

+<D 105 ْ 22’

Az DE = 134 ْ 27’

Az DE = 134 ْ 27’

+ 180ْ

Az ED = 314 ْ 27’

+<E 108 ْ 28’

Az EA = 422 ْ 55’

- 360 ْ

Az EA = 62 ْ 55’Finish

CheckAz EA = 62 ْ 55’

+ 180ْ

Az AE = 242 ْ55’

+<A 87 ْ 05’

Az AB = 330 ْ00’

4.10: Bearing Computation:

Line BC:

(?)= 180 – (120 ْ 28’- 30 ْ )

(?)= 89 ْ 32’ in N.W quad.

i.e., N 89 ْ 32’ W

Line CD:

(?)= 118 ْ 37’- 89 ْ 32’

(?)= 29 ْ 05’ in S.W quad.

i.e., S 29 ْ 05’ W

Line DE:

=(?)180ْ) – 105ْ5ْ 22+’29ْ9ْ 05(’

=(?)45ْ5ْ 33 ’in S.E. quad.

i.e., S 45ْ 33’ E

Line EA:

(?)= 108ْ 28’- 45ْ 33’

(?)= 62ْ 55’ in N.E. quad.

i.e., N 62ْ 55’ E

Line AB:

(?)= 180 – ْ (62 ْ 55’+ 87 ْ 05’)

(?)= 30 ْ 00’ in N.W. quad.

i.e., N 30 ْ 00’ W

CHECK (Line AB was S 30 ْ 00’ E )

4.12: Magnetic Direction:

• Magnetic Direction is the horizontal angle between magnetic north and geographic north.

• Isogonic chart is line joining points of the earth surface having equal magnetic declination.

Geographic Bearing of survey Line = 15 ْ30’+ 10 ْ30’

= 26 ْ00`