Question

The bearing of a line is 48\(^{\circ}\) 20' 30". The declination of the location is 2\(^{\circ}\) 30' E. The direction of true north is

• A. 45\(^{\circ}\) 50' 30"
• B. 50\(^{\circ}\) 50' 30"
• C. 45\(^{\circ}\) 50' 20"
• D. 50\(^{\circ}\) 50' 20"

Hint:

Remember the rhyme:
"Declination East, Magnetic Least" (MB is smaller than TB).
"Declination West, Magnetic Best" (MB is larger than TB).
Here, declination is East, so the True Bearing must be larger than the Magnetic Bearing.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question provides a magnetic bearing and a magnetic declination and asks for the true bearing of the line.
The phrasing "The direction of true north is" is slightly confusing, but it is asking for the bearing relative to true north.

Step 2: Key Formula or Approach:
-

Magnetic Bearing (MB): The bearing measured relative to Magnetic North.
Given MB = 48\(^{\circ}\) 20' 30". -

Magnetic Declination: The angle between True North and Magnetic North.
Given Declination = 2\(^{\circ}\) 30' E (East). -

True Bearing (TB): The bearing measured relative to True North.
The relationship is: \( \text{True Bearing} = \text{Magnetic Bearing} \pm \text{Declination} \).
Use '+' for East declination and '-' for West declination.

Step 3: Detailed Explanation:
The declination is 2\(^{\circ}\) 30'

East.
This means the Magnetic North is 2\(^{\circ}\) 30' to the east of True North.
Therefore, to get the True Bearing, we must add the declination to the Magnetic Bearing.
\[ \text{TB} = \text{MB} + \text{East Declination} \] \[ \text{TB} = 48^{\circ} 20' 30" + 2^{\circ} 30' 00" \] Adding the degrees, minutes, and seconds separately: \[ \text{TB} = (48+2)^{\circ} (20+30)' (30+00)" \] \[ \text{TB} = 50^{\circ} 50' 30" \]

Step 4: Final Answer:
The true bearing of the line is 50\(^{\circ}\) 50' 30".
This corresponds to option (B).