Since we are fairly familiar with the four main directions - **North, South, East and West** - there is not going to be an issue in identifying
them, as long as we know where **North** is.

The problem, however, arises when we have to express the direction between any two of them - and as a numerical value for accuracy.

By expressing the direction in terms of **bearings** we can overcome a catalogue of practical difficulties in the field of navigation.

Just look at the sky in the following animation near Heathrow, in the United Kingdom; how do aircraft controllers stop these planes from collisions in a saturated sky? It is the role of **three-figure-bearings** that help keep the order in our skies.

This tutorial helps you understand the concept effectively using an *interactive* programme.

A **bearing** is defined as an *angle* measured *clockwise * from the **north direction.**

A bearing is usually expressed in three numbers; therefore, it is called **3-number-bearing.**

**E.g.**

30^{0} is expressed as 030^{0}.

130^{0} is expressed as 130^{0}.

330^{0} is expressed as 330^{0}.

0^{0} 360^{0}

**E.g.1**

The bearing of B from A is 020^{0}. Find the bearing of A from B.

The bearing of A from B = 180 + 20 = 200^{0}.

**E.g.2**

The bearing of B from A is 120^{0}. Find the bearing of A from B.

The bearing of A from B = 360 - 60 = 300^{0}.

**E.g.3**

The bearing of B from A is 220^{0}. Find the bearing of A from B.

The bearing of A from B = 040^{0}.

**E.g.4**

The bearing of B from A is 310^{0}. Find the bearing of A from B.

The bearing of A from B = 180 - 50 = 130^{0}.

**E.g.5**

The following is a map of a part of the United Kingdom. Calculate the bearings of the following cities:

- Bristol from Birmingham
- Birmingham from London
- London from Bristol

- The bearing of Bristol from Birmingham = 180 + 22 = 202
^{0}. - The bearing of Birmingham from London = 360 -45 = 315
^{0}. - The bearing of London from Bristol = 087
^{0}.

**Practice 1:**

By using a *protractor* on the screen, find the following bearings:

- Birmingham from Bristol
- Bristol from London
- London from Birmingham

**Practice 2:**

By using a *protractor* on the screen, find the following bearings:

- Mannar from Kandy
- Kandy from Galle
- Mannar from Galle

This is a vast collection of tutorials, covering the syllabuses of GCSE, iGCSE, A-level and even at undergraduate level.
They are organized according to these specific levels.

The major categories are for core mathematics, statistics, mechanics and trigonometry. Under each category, the tutorials are grouped according to the academic level.

This is also an opportunity to pay tribute to the intellectual giants like Newton, Pythagoras and Leibniz, who came up with lots of concepts in maths that we take for granted today - by using them to serve mankind.

~~"There's no such thing as a free lunch."~~

The best things in **nature** are free with no strings attached - fresh air, breathtakingly warm sunshine, scene of meadow on the horizon...

Vivax Solutions, while mimicking nature, offers a huge set of tutorials along with interactive tools for free.

Please use them and excel in the sphere of science education.

Everything is free; not even **registration** is required.

Maths is challenging; so is finding the right book. K A Stroud, in this book, cleverly managed to make all the major topics crystal clear with plenty of examples; popularity of the book speak for itself - 7^{th} edition in print.