The bearings of two lines AB and AC measured by using a surveyor’s compass are S 26° 40’ E and N 18° 30’ W, respectively. The value of ∠BAC measured in clockwise direction is ________. 

Explanation:

Included angle BAC = FB_AC (Fore Bearing of AC) - BB_BA (Back Bearing of BA)

Given data,

The bearing of line AB = S 26º 40' E = (WBC)

The bearing of line AC = N 18º 30' W = 341º 30' (WCB)

Now,

The bearing of line BA = 180º- 153º 20' = 26º 40' (WBC)

FB_AC (Fore Bearing of AC) = N 18º 30' W = 341º 30'

BB_BA (Back Bearing of BA) = 180° - 26º 40'  = 153°20'

∴ Included angle = 341º 30' - 153°20' = 188º 10'Shortcut Trick The included angle is exterior when we go in the CLOCKWISE direction.

The included angle is given as (By Visual Inspection as shown in diagram) 

\(\angle BAC =341^\circ 30' -153^\circ 20' =188^\circ10'\)

Key Points

Fore Bearings (F.B.) and Back Bearings (B.B.)

• Every line has two bearings; one is observed at each end of the line.
• The bearing of a line taken in the survey's progress or the forward direction is the line's fore or forward bearing (F. B).
• Its bearing taken in the reverse or opposite direction is reverse or back bearing (B.B).

​In Whole Circle Bearing (W.C.B.)

• B.B of a line= F.B ± 180°
• (+) plus sign if the given F.B. is less than 180° and the (-) minus sign if it exceeds 180°.

In Reduced Bearing (R.B.)

• F.B. and B.B. are numerically equal but with opposite cardinal points.
• Therefore, B. B of a line may be obtained by simply substituting N for S or S for N and E for W or W for E in its fore bearings.

Included Angle

When two lines meet at a point, the angle between them is included angle. It is an angle measured clockwise from the preceding traverse line to the forward line.

• In a clockwise traverse, the included angle is the exterior angle.
• In an anticlockwise traverse, the included angle is the interior angle