Question

The magnetic bearing of a line AB is \(S\,32^\circ E\) and the magnetic declination is \(4^\circ E\). What is the true bearing of the line AB?

• A. \(S\,36^\circ E\)
• B. \(N\,36^\circ E\)
• C. \(S\,28^\circ E\)
• D. \(N\,28^\circ E\)

Hint:

To convert magnetic bearing to true bearing, \[ \boxed{ \text{TB}=\text{MB}\pm\text{Declination} } \] (Add east declination or subtract west declination according to the adopted convention.)

Answer 1

The Correct Option is C

Step 1: Convert the magnetic bearing to whole-circle bearing (WCB). Given magnetic bearing: \[ S\,32^\circ E. \] Its WCB is \[ 180^\circ-32^\circ=148^\circ. \]

Step 2: Apply the magnetic declination. For an easterly declination, \[ \text{True Bearing} = \text{Magnetic Bearing} - \text{Declination}. \] Hence, \[ 148^\circ-4^\circ = 144^\circ. \] Converting \(144^\circ\) back to reduced bearing, \[ 180^\circ-144^\circ = 36^\circ. \] Thus the true bearing is \[ \boxed{S\,36^\circ E.} \] Therefore, \[ \boxed{(A)} \] is the mathematically correct answer. Note: The provided answer key marks option (C), but based on the standard relation \[ \boxed{\text{TB}=\text{MB}+\text{East Declination}}, \] (or equivalently using the appropriate convention), the correct true bearing is \[ \boxed{S\,36^\circ E.} \]