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How to calculate the angles from the bearings

Techno Upendra

 calculate the angles from bearings
There are two systems of mention of bearings.

A. Whole Circle System:- In the whole circle system the bearing of a line measured from the north point of the reference meridian to the line in a clockwise direction.
It has an angle between 0° to 360°.
whole circle bearing

In the figure, the whole circle bearing is 240° from the north.

B.Quadrantal System:-In the quadrant system the bearing of a line is measured clockwise or counterclockwise from the north point or south point. Toward the east or west direction. It has an angle between 0°to90°.
Quadrant bearing

In the above picture, the line AB falls in I quadrant. AC is in ii quadrant, AD in iii quadrants, AE in iv quadrants, The angle making of these line from north and south is called reduced bearing.

In the above picture reduced bearing AB=N30E°, AC=S40°E, AD=S30°W, AE=N25°W.
Method of Calculation quadrant bearing see also:-
fore bearing and back bearing

Fore and Back Bearing:- Every line has two bearings. The bearing of a line in the direction of the progress of the survey is called the fore or forward bearing and the bearing of the opposite direction is known as the back or reverse bearing(B.B)

Back bearing= Fore bearing (+),(-) 180°.

In the quadrantal system, the fore and back bearing are numerical equal but with opposite quadrant system.
If the fore bearing AB line is N 40° E, then back bearing of the line AB is S 40° W.

Calculation of angles from bearing
Case l:-Given the whole
circle bearing of lines.
Subtract smaller angles from the greater. The difference will give the interior angle if it is less than 180°. If the difference exceeds 180°, It will be the exterior angle. Obtain the interior by subtracting the difference from 360°.
If any lines AB,41°, AC, 115 °
Angle BAC= Bearing of AC-Bearing of AB=115°-41°=74°.
Case ll:- Given the reduced bearing of Lines:

(a) if the lines are on the same side of the same meridian. See above picture
Included angle= difference of the bearing of OA and OB.

(b) if the lines are on the same side of the different meridians, included angle=180°-sum of the two reduced bearings.

(C) if the lines are on different sides of the different meridian.
  Included angle=180°-difference of the two reduced bearings.
  BOA=180°-difference of the bearing OB and OA.

(d) if the lines are on opposite sides of the same meridian.
 The included angle= sum of the two reduced bearing.
BOA= sum of the bearings of OB and OA.