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
- A189° 10'
- B188° 10'Correct
- C134° 10'
- D135° 10'
Solution
Concept
Convert quadrantal bearings to whole circle bearings (WCB), then subtract to get the clockwise angle.
Formula
Clockwise ∠BAC = WCB of AC − WCB of AB (add 360° if negative)
Step-by-step solution
1. AB = S 26°40' E, so WCB of AB = 180° − 26°40' = 153°20'. 2. AC = N 18°30' W, so WCB of AC = 360° − 18°30' = 341°30'. 3. Clockwise angle from AB to AC = 341°30' − 153°20' = 188°10'. 4. So ∠BAC = 188°10'.
Explanation
First change both bearings to whole circle bearings. AB is 153°20' and AC is 341°30'. Going clockwise from AB to AC, the angle is 341°30' − 153°20' = 188°10'.
Why the other options are wrong
A: 189°10' is a 1° arithmetic error. C and D: 134°10' and 135°10' come from wrong conversion of the bearings to WCB.
Shortcut
The two lines are nearly opposite, so the angle is 180° + (26°40' − 18°30') = 188°10'.
Common mistake
Using 180° + 26°40' for the S-E bearing, or subtracting in the wrong order, which gives the anticlockwise angle 171°50'.
Correct answer: B) 188° 10'