Questions
Question
A sailing ship leaves harbour and sails on a bearing \(047^{o}\) for \(6.5km\). It then changes course to a bearing of \(126^{o}\) and sails for \(5.7km\).
The captain now wishes to return to harbour. At what bearing must he sail to go directly to harbour?
- choose an appropriate scale such as \(1cm\) represents \(1\,km\)
- choose any point on your paper to be the harbour
- mark the North line on the harbour
- use a protractor to mark the bearing \(047^{o}\) and draw a line of \(6.5cm\) from the harbour through this point
- mark a new North line at the end of the 1st leg (new position of ship)
- use a protractor to mark the bearing \(126^{o}\) and draw a line of \(5.7cm\) from the new position through this point
- draw a new North line at the end of the 2nd leg
- to get the return bearing join up the end of the 2nd leg with the harbour
- use a protractor to measure the bearing of this line
The bearing back to harbour should be around \(260^{o}\)
Question
Two flight control centres are \(75km\) apart.
Control Centre \(A\) is directly West of Control Centre \(B\).
A plane is on the screens of both centres.
The plane is at a bearing of \(057^{o}\) from Control Centre \(A\) and a bearing of \(320^{o}\) from Control Centre \(B\).
Which control centre is the plane nearest to? (Justify the answer).
Choose an appropriate scale (\(1cm\) represents \(10km\)).
As the control centres are on a West/East line we can draw a line of \(7.5cm\) with \(A\) and \(B\) at each end.
Make North lines at \(A\) and \(B\) and mark each bearing with a protractor.
Extend the bearing lines from \(A\) and \(B\) until they cross. (This is where the plane is).
Measure the distance from the plane to each control tower and convert back to kilometres using the scale. Write down which control centre is nearest to the plane.
The working is the justification for the answer to this question.
The answer is Control Centre \(B\).