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Assignment :- 1 Angle Calculation From Bearing

 

  1. Traverse: A sequence of connected survey lines forming a closed loop.

  2. Interior Angle: The angle formed between two consecutive sides of a traverse.

  3. Clockwise Traverse: The order of points is clockwise.

  4. Counterclockwise Traverse: The order of points is counterclockwise.

Method:

  1. Measure the included angles using a theodolite or compass.

  2. For clockwise traverses:

    • Subtract the smaller bearing from the larger one.

    • If the difference is less than 180°, it’s an interior angle.

    • If the difference exceeds 180°, it’s an exterior angle.

    • If negative, add 360° to get the whole circle bearing.

  3. For counterclockwise traverses:

    • Add the smaller bearing to the larger one.

    • Follow the same rules as above.

Calculating Fore Bearing and Back Bearing:

  1. Fore Bearing (FB): The bearing of a line from the starting point to the ending point.

  2. Back Bearing (BB): The bearing of the same line in the opposite direction.

  3. Whole Circle Bearing System (WCB): Bearings measured clockwise from the north direction (0° to 360°).

Method:

  1. For WCB:

    • BB = FB + 180° if FB < 180°

    • BB = FB - 180° if FB > 180°

  2. For Quadrantal Bearings:

    • BB = Numerically equal to FB (change N for S and E for W).

Sum of Interior Angles in a Polygon:

  1. Regular Polygon: All interior angles are equal.

  2. Irregular Polygon: Interior angles may vary.

  3. Formula:

    • Sum of interior angles = (n - 2) × 180°

    • Where ‘n’ is the number of sides.

    • Examples:

      • Triangle: 180°

      • Quadrilateral: 360°

      • Pentagon: 540°

      • Hexagon: 720°

Remember, the sum of interior angles remains constant regardless of polygon type!

 

Assignment :- 1

A. 1. The fore bearings of the sides of the closed traverse ABCDEA are as follows: Calculate the Internal Angles from the given data.

AB: 107° 15’ (from point A to point B)
BC: 22° 00’ (from point B to point C)
CD: 281° 30’ (from point C to point D)
DE: 181° 15’ (from point D to point E)
EA: 124° 45’ (from point E back to point A)

2.

AB: 45° 15’ (from point A to point B)
BC: 117° 00’ (from point B to point C)
CD: 281° 30’ (from point C to point D)
DE: 320° 15’ (from point D to point E)
EA: 123° 45’ (from point E back to point A)

3.

AB: 125° 65’ (from point A to point B)
BC: 218° 37’ (from point B to point C)
CD: 310° 34’ (from point C to point D)
DE: 12° 14’ (from point D to point E)
EA: 250° 16’ (from point E back to point A)

 

B. Calculate the Included Angle <AOB

Question    Bearing OA    Bearing OB
1                    40° 15′           220° 45′
2                    80° 30′           300° 20′
3                    120° 0′          240° 30′
4                    160° 15′        340° 45′
5                    50°  10′         230° 20′
6                    70°  0′           250° 30′
7                    110° 15′        290° 45′

 

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