大象传媒

NavigationDistance and direction

A navigation course can be planned using a map or plan. Using bearings and distance, this course can be presented in graphical form. Unknown distances and bearings can be calculated from the diagram.

Part of Application of MathsMeasurement skills

Distance and direction

Navigation requires distance and direction. Direction is usually given using three-figure bearings.

Example

Map of an island and a harbour. Scale represents 1cm:1km

A boat leaves harbour to sail around a nearby island. The journey is split into four legs (parts).

The first two legs are given in the table.

BearingDistance
1st leg\(063^{o}\)\(5.3km\)
2nd leg\(105^{o}\)\(7.0km\)
3rd leg
4th leg
1st leg
Bearing\(063^{o}\)
Distance\(5.3km\)
2nd leg
Bearing\(105^{o}\)
Distance\(7.0km\)
3rd leg
Bearing
Distance
4th leg
Bearing
Distance

To complete the table, first draw a scale diagram.

Step one

Show the first two legs of the journey on the diagram.

5.1km line on 63 degree bearing leads to 7km line on 105 degree bearing. Purple cross at bottom of image.

Step two

Draw the 3rd and 4th legs on the diagram so that the ship travels to the point marked X and then on to the harbour.

5.1km line on 63 degree bearing leads to 7km line on 105 degree bearing. 5.9km line on 238 degree bearing touches purple cross.
5.1km line on 63 degree bearing leads to 7km line on 105 degree bearing. 5.9km line on 238 degree bearing touches purple cross. 6.8km line at 293 degree bearing joins up with start.

Part three

Complete the table for these two legs showing the bearings and distance.

BearingDistance
1st leg\(063^{o}\)\(5.3km\)
2nd leg\(105^{o}\)\(7.0km\)
3rd leg\(238^{o}\)\(5.9km\)
4th leg\(293^{o}\)\(6.8km\)
1st leg
Bearing\(063^{o}\)
Distance\(5.3km\)
2nd leg
Bearing\(105^{o}\)
Distance\(7.0km\)
3rd leg
Bearing\(238^{o}\)
Distance\(5.9km\)
4th leg
Bearing\(293^{o}\)
Distance\(6.8km\)

Related links