Clossing error in theodolite traversing, calculations of bearings from angles, theodolite traversing problems

Clossing Error:-

                                   The distance by which a traverse fails to close is known as clossing error.

Calculation of bearings from angles:-

      The bearing of traverse may be calculated as 

1. Included angle method

2. Deflection angle method

1.) Included angle Method :-

 Q. The interior angles of traverse ABCDE are measured as follow:-  

           ∠A = 76 12  , ∠B = 112 12 , ∠C = 98 12 40  , ∠D = 130 9 20  , ∠E = 123 14

the bearing of initial line AB is observed as 217 50 20 find out the bearing of remaining side.

Given.,

             ∠A = 76 12

             ∠B = 112 12

             ∠C = 98 12 40

             ∠D = 130 9 20

             ∠E = 123 14

F.B. of AB = 217 50 20

B.B. of AB =  217 50 20 – 180

                    = 37 50 20

F.B. of BC =  ∠B + B.B of AB

                   = 112 12 + 37 50 20

                   = 150 2 20

B.B. of BC = 150 2 20 + 180

                    = 330 2 20

F.B. of CD = (  ∠C + B.B of BC ) – 360

                    =  ( 98 12 40 + 330 2 20 ) – 360

                    = 428 15 – 360

                    = 68 15

B.B. of CD = 68 15 + 180

                    = 248 15

F.B of DE = ( ∠D + B.B. of CD ) – 360

                   = ( 130 9 20 + 248 15 ) – 360

                   = 378 24 20 – 360

                   = 18 24 20

B.B. of DE = 18 24 20 + 180

                    = 198 24 20

F.B of EA =  ∠E + B.B. of DE

                   = 123 14  + 198 24 20

                   = 321 38 20

B.B. of EA = 321 38 20 – 180

                    = 141 38 20

 

CHECK :-

                   F.B. of AB = B.B. of EA +  ∠A

                  217 50 20 = 141 38 20 + 76 12

                  217 50 20 = 217 50 20

2.) By deflection angle :-

Q.  The following deflection angles were measured in running a traverse from A to F.

Station	DEflection angle
b	23 47   R
c	18 19   L
D	37 20   R
E	15 38   R
F	10 12   L

 If  the true bearing of AB is N 60 18 E calculate the bearing of remaining side.

F.B. of BC = F.B. of AB + deflection at ∠B

                   = 60 18 + 23 47

                   = 84 5

F.B. of CD = F.B. of BC – deflection at ∠ C

                    = 84 5 – 18 19

                    = 65 46

F.B. of DE = F.B. of CD + deflection at ∠ D

                    = 65 46 + 37 20

                    = 103 6

F.B. of EF = F.B. of DE + deflection at ∠ E

                   = 103 6 + 15 30

                   = 118 44

F.B. of FG = F.B. of EF – deflection at ∠ F

                   = 118 44 – 10 12

                   = 108 32

CHECK :-

                   F.B. of last bearing = F.B. of first line + sum of all Right deflection – sum of all Left deflection.

                               =  60 18 + 76 45 – 28 31

                               = 108 32