What is the primary difference between a standard geometric angle and a bearing?

Standard angles are typically measured anti-clockwise from the positive x-axis (East), whereas bearings are always measured clockwise from North.

How does the bearing of 'A from B' relate to the bearing of 'B from A'?

They are back bearings of each other, meaning they differ by exactly $180^{\circ}$. This is because the North lines at A and B are parallel, creating interior or alternate angle relationships.

Why is a bearing of $45^{\circ}$ written as $045^{\circ}$?

Bearings must always be expressed as three-figure values to maintain a consistent format in navigation, preventing confusion with other types of measurements or coordinates.

What is the most common error when measuring a bearing with a protractor?

Measuring anti-clockwise from North or measuring from the horizontal (East-West) line instead of the vertical North line.

What happens if you calculate a back bearing by subtracting from $180^{\circ}$ instead of adding/subtracting $180^{\circ}$?

You will find the supplementary angle rather than the opposite direction. A back bearing requires a $180^{\circ}$ rotation to face the exact opposite way.

If a bearing is $210^{\circ}$, what is the back bearing?

The back bearing is $030^{\circ}$. Since $210 > 180$, you subtract $180$ ($210 - 180 = 30$) and apply the three-figure rule.

Define the three mandatory rules for writing a bearing.

1. Measured from North. 2. Measured clockwise. 3. Written with three digits.

In the phrase 'The bearing of X from Y', where should the North line be drawn?

The North line must be drawn at point Y, as that is the starting reference point for the measurement.

What geometric property of North lines allows us to use interior angles ($180^{\circ}$) to find bearings?

The assumption that all North lines are parallel to each other, which makes the line connecting two points a transversal.

What is the bearing for the compass direction South-West?

The bearing is $225^{\circ}$. This is calculated as $180^{\circ}$ (South) plus $45^{\circ}$ (halfway to West).

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Geometry & Measures

Bearings

Summary

Bearings are a standardized system of angular measurement used in navigation and geometry to describe the direction of one point relative to another. They are defined by three strict rules: they must be measured from North, in a clockwise direction, and expressed as a three-figure value.

1. Definition & Core Concepts

Standard Definition: A bearing is an angle measured from a fixed reference line (North) to a line of travel or a specific destination. This system provides a universal language for pilots, sailors, and surveyors to communicate directions without ambiguity.
The Three Rules: For a measurement to be considered a formal bearing, it must be measured clockwise from North and always written using three digits (e.g., $045^{\circ}$ instead of $45^{\circ}$ ).
Reference Points: The phrasing 'the bearing of B from A' is critical; it indicates that the observer is standing at point A, and the North line must be drawn at point A to measure the angle toward B.

Diagram showing a bearing measured clockwise from a North line at Point A toward Point B.

2. Underlying Principles

3. Methods & Techniques

4. Key Distinctions

5. Exam Strategy & Tips

6. Common Pitfalls & Misconceptions