The true reduced bearing is N 5°0’W and the magnetic declination is 2°E. Find the true bearing in the whole circle bearing system.

🧭 Understanding the Core Concept

This question tests the conversion between two bearing systems: the Reduced Bearing (RB) or Quadrantal Bearing (QB) system, and the Whole Circle Bearing (WCB) system. It also includes extraneous information (magnetic declination) to check if the core concept is understood.

• True Bearing: A bearing measured relative to the true geographic North.
• Magnetic Declination: The angle between true North and magnetic North. It is only used to convert between true bearings and magnetic bearings.

🔬 Step-by-Step Calculation

Step 1: Analyze the Given Information

• True Reduced Bearing = N 5° W
• Magnetic Declination = 2° E (This is not needed for the calculation)

Step 2: Identify the Quadrant

The bearing N 5° W is in the fourth quadrant (North-West), as it is measured 5° West of the North line.

Step 3: Convert from Reduced Bearing (RB) to Whole Circle Bearing (WCB)

The formula for converting an RB in the North-West quadrant to a WCB is:

WCB = 360° - (Angle from North)

Applying the values:

WCB = 360° - 5° = 355°

💡 Key Insight: Why Magnetic Declination is Irrelevant Here

The question provides the true reduced bearing and asks for the true whole circle bearing. Since we are converting between two types of true bearings, the magnetic declination is not used. It would only be necessary if we were asked to find a magnetic bearing from a true bearing, or vice versa.