Compute the interior angle of traverse:

During the compass survey a traverse ABCDE was run. The bearings as measured are recorded in table given below. Compute the interior angle of traverse. Also calculate closing error if any.

Solution

(a)        Back bearing of AB = 286^o 19′

Fore bearing of BC = 27^o 06′

Included angle ABC = 286^o 19′ - 27^o 06′ = 259^o 13′ > 180o Exterior angle.

∠ B = 360^o - 259o13′ = 1000 47′ Interior angle.

(b)       Back bearing of BC = 207^o 06′

Fore bearing of CD = 279^o 42′

Included angle = Difference of bearings; ∠ C = 72^o 36′ < 180^o

Interior angle.

(c)        Back bearing of CD = 99^o 42′

Fore bearing of DE = 193^o 17′

Included angle = Difference of bearing; ∠ D = 93^o 35′ < 180^o Interior angle.

Figure

(d)       Back bearing of DE = 13^o 17′

Fore bearing of EA = 126^o 32′

Included angle = ∠ E = Difference of bearings

= 113^o 15′ < 180o (Interior angle).

(e)        Back bearing of EA = 306^o 32′

Fore bearing of AB = 106^o 19′

Included angle = ∠ A = Difference of bearings

= 200^o 13′ > 180^o (Exterior angle).

= 360^o - 200^o 13 ′ = 159^o 47′ (Interior angle) Check Σ ∠ = ∠ A +∠ B +∠ C + ∠ D + ∠ E

= 159^o 47′ + 100^o 47′ + 72^o 36′ + 93^o 35′ + 113^o 15′ = 540^o 00′

(2N - 4) × 90 ^o = (10 - 4) × 90 = 540^o

∴ There is no closing error in the traverse.