Meaning of Bearing

Bearing is a way of finding or showing direction. It tells us where one place is from another place by using angles.

When we want to move from one place to another, we must know the direction. Bearing helps us to describe that direction exactly by measuring an angle from the North line.

In simple words: Bearing means “the angle measured clockwise from the North direction to the line that joins two places.”

For example, if you are standing at point A and you want to go to point B, you draw a line pointing North at point A. Then you measure the angle clockwise (like the hand of a clock) until you reach the line joining A and B. That angle is called the bearing of B from A.

Important Facts About Bearing

All bearings are measured from the North direction. We always start counting the angle from the North line.

Bearings are measured clockwise. Clockwise means in the same direction that the hands of a clock move.

Bearings are written in three figures (three digits). This helps us to write them neatly and clearly.

For example:

• 5° is written as 005°


• 35° is written as 035°


• 90° is written as 090°

Bearings are always between 000° and 360°.

000° or 360° means North

090° means East

180° means South

270° means West

So, a full circle has 360°, and that circle shows all the possible bearings.

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MAJOR AND MINOR CARDINAL POINTS

Meaning of Cardinal Points

Cardinal points are the main directions that show how to locate one place from another. They are shown on a compass.

A compass is an instrument used for finding directions. It has a needle that always points to the North.

The Four Major Cardinal Points

There are four major cardinal points:

• North (N)


• East (E)


• South (S)


• West (W)

These four points divide the compass into four equal parts, and each part is 90° apart.

Bearings of the Major Cardinal Points:

• North → 000° or 360°


• East → 090°


• South → 180°


• West → 270°

The Four Minor (Intermediate) Cardinal Points

Between each pair of major points, there is a middle direction called a minor or intermediate cardinal point.

The four minor cardinal points are:

• Northeast (NE) – between North and East


• Southeast (SE) – between South and East


• Southwest (SW) – between South and West


• Northwest (NW) – between North and West

Now we have eight main directions on a compass.

Bearings of the Minor Points:

• NE → 045°


• SE → 135°


• SW → 225°


• NW → 315°

Diagram of the Eight Cardinal Points

           N (000°)
             |
             |
   NW(315°)  |  NE(045°)
             |
W(270°) -----+----- E(090°)
             |
             |
   SW(225°)  |  SE(135°)
             |
             |
           S (180°)

Importance of Cardinal Points

1. They help us to know and describe directions.


2. They are used in maps and navigation.


3. They help pilots, sailors, and travelers to move in the right direction.


4. They are used in geography to describe where one place is located.


5. They are used in surveying and construction to show directions and positions.

Relationship Between Cardinal Points and Bearing

Cardinal points and bearings are closely connected. Each direction on the compass has a bearing value.

Direction	Bearing
North	000° or 360°
Northeast	045°
East	090°
Southeast	135°
South	180°
Southwest	225°
West	270°
Northwest	315°

So, cardinal points show general directions, while bearings show exact angles between places.

Types of Bearing

There are two main types of bearings that we learn in JSS Mathematics:

1. Compass Bearing (or Ordinary Bearing)

Compass bearing uses the letters N, S, E, and W to show direction. The angle is always less than 90°. We start from North or South, then turn East or West.

Compass Bearing	How to Read It
N 40° E	From North, turn 40° toward East
N 25° W	From North, turn 25° toward West
S 30° E	From South, turn 30° toward East
S 45° W	From South, turn 45° toward West

If a point B is N 40° E from point A, start at A, look North, then turn 40° toward East. That is where B is located.

2. Three-Figure Bearing

Three-figure bearing uses only numbers (no N, S, E, or W). We measure the angle clockwise from the North direction and write it in three digits.

Direction	Bearing
North	000° or 360°
East	090°
South	180°
West	270°

How to Change Compass Bearing to Three-Figure Bearing

Compass Bearing	Formula	Example	Answer
N θ E	θ	N 40° E	040°
N θ W	360° − θ	N 20° W	340°
S θ E	180° − θ	S 30° E	150°
S θ W	180° + θ	S 45° W	225°

Bearing of A from B and Bearing of B from A

“Bearing of B from A” means you are standing at A and looking toward B.

“Bearing of A from B” means you are standing at B and looking toward A. They are not the same. They are in opposite directions.

To find the opposite bearing:

• If the bearing is less than 180°, add 180°.
• If the bearing is more than 180°, subtract 180°.

Examples:

• Bearing of B from A = 065° → Bearing of A from B = 065° + 180° = 245°


• Bearing of B from A = 300° → Bearing of A from B = 300° − 180° = 120°

How to Find Bearing from a Map or Diagram

1. Mark the two points (example: A and B).


2. Draw a line pointing straight North from the starting point.


3. Draw a line from that point to the other point.


4. Measure the angle clockwise from the North line to the line joining the two points.


5. Write your answer in three figures.

Uses of Bearings

1. Used by pilots and sailors to find directions while traveling.


2. Used in surveying to measure land and mark boundaries.


3. Used in map reading to locate towns and landmarks.


4. Used in engineering and construction to draw plans.


5. Used in geography to describe where one place is located from another.

Common Mistakes Students Make

• Measuring the angle anticlockwise instead of clockwise.


• Forgetting to start from the North line.


• Writing bearings in two digits instead of three (e.g., 40° instead of 040°).


• Mixing up “bearing of A from B” and “bearing of B from A.”


• Using the wrong formula when converting compass bearings.

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Questions Examples on Bearing

Example 1: Find the three-figure bearing of A from O if A is N 40° E from O

Step 1: Compass bearing is N 40° E → start at North and turn 40° toward East.

Step 2: Use formula for N θ E → θ = 40°

Step 3: Write in three-figure format → 040°

Answer: 040°

           N
           |
           | 40°
           |  
O ---------A

Example 2: Find the three-figure bearing of B from O if B is S 30° E from O

Step 1: Compass bearing is S 30° E → start at South and turn 30° toward East.

Step 2: Use formula S θ E → 180° − θ = 180° − 30° = 150°

Step 3: Three-figure bearing → 150°

Answer: 150°

           N
           |
           |
           |
           |
O ---------B
           \
            \
             S

Example 3: The bearing of C from D is 300°. Find the bearing of D from C

Step 1: Given bearing = 300°

Step 2: Reverse bearing = 300° − 180° (since >180°) = 120°

Answer: 120°

Example 4: A ship sails from point P on a bearing of 070° to point Q. Find the bearing of P from Q

Step 1: Given bearing = 070°

Step 2: Reverse bearing = 070° + 180° = 250°

Answer: 250°

Example 5: Find the bearing of a point R which lies due west of S

Step 1: West direction → bearing = 270°

Answer: 270°

S -------- R
0°       270°

Example 6: Convert N 20° W to three-figure bearing

Step 1: Compass bearing = N 20° W

Step 2: Use formula N θ W → 360° − θ = 360° − 20° = 340°

Answer: 340°

Example 7: Convert S 45° W to three-figure bearing

Step 1: Compass bearing = S 45° W

Step 2: Use formula S θ W → 180° + θ = 180° + 45° = 225°

Answer: 225°

Example 8: A point M lies Northeast of N. Find the bearing

Step 1: Northeast → halfway between North and East

Step 2: Bearing = 045°

           N
           |
           |
           |
           |
N ---------M

Example 9: Reverse the bearing 150°

Step 1: Given bearing = 150° (less than 180°)

Step 2: Add 180° → 150° + 180° = 330°

Answer: 330°

Example 10: Find the bearing of a point K that lies Southwest of L

Step 1: Southwest is between South and West

Step 2: Bearing = 225°

           N
           |
           |
           |
L ---------K

Practice Questions

1. Change N 25° E to a three-figure bearing.


2. Change S 40° W to a three-figure bearing.


3. Find the reverse bearing of 070°.


4. What is the bearing of due South?


5. What is the bearing of due East?


6. If the bearing of B from A is 135°, find the bearing of A from B.


7. Change N 75° W to a three-figure bearing.


8. A point C lies S 10° E from D. What is the three-figure bearing of C from D?

Summary

1. Bearing is a way of showing direction using angles measured clockwise from North.


2. It helps us to find one place from another.


3. There are four major and four minor cardinal points.


4. Bearings are written in three figures (000°–360°).


5. Bearings are very important in navigation, geography, and surveying.


6. Always measure clockwise and start from North.