NZ Level 6 (NZC) Level 1 (NCEA)
topic badge
Bearings
Lesson

In surveying and air navigation, bearing are used to help identify the location of an object.

The four main directions of a compass are known as cardinal directions. They are north (N), east (E), south (S) and west (W).

Three-figure (True) Bearings

A three-figure bearing are:

  • measured from north ($N$N)
  • measured in a clockwise direction
  • written using three figures

 A $T$T is often but not always used to indicate a true bearing. If the angle measure is less than $100^\circ$100° it would be written something like 040° or 040°T.

To use true bearing to describe the location of a plane at point $B$B from the airport at point $A$A :

  1. place the centre of a compass on the starting point, in the case the airport.
  2. starting at North, rotate clockwise until we get to the line $AB$AB
  3. write angle as the true bearing of point $B$B.

 

The true bearing of $B$B from $A$A is $127^\circ$127° or $127^\circ$127°$T$T.

The diagram below describes the bearing of $P$P from $O$O. Rotating clockwise from North, we get an angle of $55^\circ$55°

Since this measure is less than three digits, we put a 0 in front of it so the true bearing of $P$P is 055°. Consider the true bearing of $O$O from $P$P  . Since angle of elevation is equal to angle of depression and we are starting at $P$P the true bearing would be $180+55=235^\circ$180+55=235°.

 

Compass Bearings

A compass bearing describes the location of a point using:

  • the starting direction of either north or south;
  • the acute angle needed to rotate
  • the direction to rotate, east or west.

To describe the position of point $B$B from $A$A we would say:

"Starting at South, I then rotate $53$53° towards East."

 

We can write this mathematically as:

$S$S$53$53°$E$E

 

Example

Find the three-figure and the compass bearings of point $P$P from $O$O.

Solution:

Three-figure bearing:

Starting at North rotate in a clockwise direction.

$360^\circ-47^\circ=313^\circ$360°47°=313° 

The three-figure bearing of $P$P from $O$O is $313^\circ$313°$T$T.

Compass Bearing

Point $P$P is closest to North, so starting at North, rotate $47^\circ$47° towards West.

The compass bearing of $P$P from $O$O is $N$N$47^\circ$47°$W$W.

 

Which one first?

The bearing needed or used completely depends on which position comes first.  Have a look at the investigation below, it quickly shows you how the angle changes depending on if we are measuring the bearing of A from B or B from A.

 

Let's have a look at these worked examples.

Question 1

Consider the point $A$A.

  1. Find the true bearing of $A$A from $O$O.

  2. What is the compass bearing of point $A$A from $O$O?

    $\editable{}$ $\editable{}$$^\circ$° $\editable{}$

Question 2

What is the true bearing of Southwest?

Question 3

In the figure below, point $B$B is due East of point $A$A. We want to find the position of point $A$A relative to point $C$C.

  1. Find the true bearing of point $A$A from point $C$C.

  2. What is the compass bearing of point $A$A from point $C$C?

    $\editable{}$ $\editable{}$$^\circ$° $\editable{}$

 

 

 

 

Outcomes

GM6-7

Use a co-ordinate plane or map to show points in common and areas contained by two or more loci

91033

Apply knowledge of geometric representations in solving problems

What is Mathspace

About Mathspace