Classwork Series and Exercises (Mathematics – JSS2): Bearing and Distance

BEARING AND DISTANCE

Compass directions

There are four main directions: north (N), south (S), east (E), and west (W). The sun rises in the east and sets in the west. If you face east and turn through an angle of 90⁰ to your left, you will face north.

If you face north and turn an angle of 90⁰ to the left, you will face west.

To face south, face east, then turn an angle of 90⁰ to the right. See the figure below.

The magnetic compass

The magnetic compass is used for finding direction. It has a magnetic needle which always points in the North direction.

Points of the compass

The figure below shows the main points of the compass.

 

Apart from the four main points, or directions: north (N), south (S), east (E) and west (W), there are also four secondary directions: north-west (NE), south-east (SE), south-west (SW) and north-west (NW). The angle between the direction N and E is 90⁰. NE is the direction mid-way between N and E. Thus the angle between N and E is 45⁰.

Exercise

1. Do the following and state the final direction that you face.
2. Face east, turn through an angle of 180⁰.
3. Face east, turn through 45⁰ to your right.
4. Face east, turn through 90⁰ to your right.
5. Face east turn through angle 90⁰ to your left.
6. What is the angle between the following directions?
7. N and S b. W and E c. NE and S d. N and W e. E and SW f. SW and W g. N and NW h. NE and SW.

Bearings

If student A is standing 5m north of student B, we say that A is north of B. We can also say that the direction of A from B is north. We use the word bearing for directions between two points.

In other words the bearing of A from B is north. Similarly, the bearing of B from A is south. This section explains the three main ways of giving bearing.

Compass bearings

Bearings are simply a way of giving directions (a bit more accurately than just relying on North, South, East and West!).

If they are given with a distance as well, then you have an exact position.

Note:

1. Bearings are always measured from North, which is 000⁰ (or 360⁰). Always draw a North line at each point to give a guide for your protractor.

2. They are always measured clockwise and must have three figures. So East is 090⁰, South is 180⁰ and West is 270⁰.

Finding a position

If you are given the bearing and position of something from a point and asked to mark it in (after which you may be asked to measure something else) then here’s what you do:

1. Draw a North line at the point you are measuring from.

2. Put your protractor on this point and line up 0⁰ with the North line. Always lean right over the paper when you’re doing this!

3. Read round the protractor clockwise until you reach the angle you want and mark it with a pencil.

4. Draw a pencil line from the point you are measuring from right through your angle point.

5. Check your scale (if there is one) and measure the distance you need along this line. Put a cross to show your position.

Don’t rub any of your pencil lines out. These help to show what you’ve done.

Here’s the kind of diagram you might have for a ship which is 8 km away from a lighthouse on a bearing of 125⁰ using a scale of 1 cm = 1 km.
Acute-angle bearings

Bearing can also be given as acute angles measured from the north (N) or south (S).