Finding Bearings and Back Bearings – Regular Polygons and Bearings (Primary 6 Mathematics) | Ganzaa

Regular Polygons and Bearings

Lessons

Primary 6 · Mathematics

Regular Polygons and Bearings

5 lessons

Lesson 5 of 5

Finding Bearings and Back Bearings

16 min

Let's begin

On a map of Rwanda, Musanze is up and to the left of Kigali. Mugisha's teacher says: "The bearing of Musanze from Kigali is about 316°." Then she asks: "So what is the bearing of Kigali from Musanze?"

Half the class answers 316° again. They are wrong, and in this lesson you will see why.

"The bearing of B from A"

The little word from tells you where to stand. To find the bearing of B from A:

Stand at A, and draw a North line through A.
Draw the straight line from A to B.
Measure the angle clockwise from the North line round to the line AB.
Write it with three figures.

In the diagram, the orange angle shows that the bearing of B from A is 060°.

The back bearing

Now stand at B and look back at A. You are looking in exactly the opposite direction, which is half a turn (180°) away. So:

if the bearing is less than 180°, add 180°;
if the bearing is 180° or more, subtract 180°.

In the diagram, the blue angle shows the bearing of A from B: 060° + 180° = 240°.

Worked example 1

Musanze is on a bearing of about 316° from Kigali. 316° is more than 180°, so the bearing of Kigali from Musanze is 316° − 180° = about 136°, roughly South-East. Check: 136° + 180° = 316°. ✔

Worked example 2

a boat crosses Lake Kivu from Rubavu to Karongi on a bearing of about 166°. To come straight back, it sails on 166° + 180° = 346°.

Worked example 3

the bearing of the health centre from Ishimwe's school is 250°. The bearing of the school from the health centre is 250° − 180° = 070°.

The angle between two bearings

Worked example 4

from the school, the market is on a bearing of 050° and the church is on a bearing of 120°. Both angles are measured from the same North line, so the angle between the two directions is 120° − 50° = 70°.

Worked example 5

from Kigali, Huye is on a bearing of about 206° and Rwamagana is on a bearing of about 091°. Huye's bearing is between 180° and 270°, so Huye is South-West of Kigali. Rwamagana's bearing is just past 090°, so it is almost due East.

Tip

"From" is where your feet are. Put the North line at the place that comes after the word from.

For the way back: add 180° if the answer stays under 360°; otherwise take 180° away.

✦

Try it yourself

The bearing of B from A is 035°. What is the bearing of A from B?
The bearing of Q from P is 290°. Find the bearing of P from Q.
Keza walks from home to school on a bearing of 180°. On what bearing does she walk home?
From a tree, a well is on a bearing of 080° and a house is on a bearing of 145°. Find the angle between them at the tree.

Answers

035° + 180° = 215°.
290° − 180° = 110°.
180° − 180° = 000° (due North).
145° − 80° = 65°.

Quick check

The bearing of B from A is 070°. What is the bearing of A from B?

What you learned today

The bearing of B from A is measured at A, clockwise from North to the line AB.
A back bearing is always 180° different: add 180° if the bearing is under 180°, and subtract 180° if it is 180° or more.
To find the angle between two directions from the same place, subtract one bearing from the other.

Sources and credits

Written by Ganzaa, including the bearing diagram and all the worked examples. The bearings between Rwandan towns are approximate values that Ganzaa calculated from the towns' map coordinates.

1"The bearing of B from A"

2The back bearing

3The angle between two bearings

Try it yourself

"The bearing of B from A"

The back bearing

The angle between two bearings