Bearings
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Calculator 1 mark
The diagram shows a harbour \(H\) and a boat \(B\).
\(B\) is west of \(H\).
State the bearing of \(B\) from \(H\).
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Calculator 1 mark
The diagram shows a school \(S\) and a mast \(R\). The bearing of \(R\) from \(S\) is marked on it.
State the compass direction of \(R\) from \(S\).
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Either paper 5 marks
Here is a map of a town.
Each square of the grid is 1 cm by 1 cm.
Scale: 1 cm represents 136 m
North is at the top of the map.
(a)Which place is exactly south east of the station?
Circle your answer.
library, market, monument, school, town hall
(b)Circle the three-figure bearing of the town hall from the station.
000° 090° 180° 270°
(c)What is the distance, in metres, from the market to the station?
(d)Why might the shortest walking distance from the market to the station be greater than your answer to part (c)?
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Calculator 2 marks
The diagram shows two points \(A\) and \(B\), with a north line drawn at each of them.
The bearing of \(B\) from \(A\) is \(127^\circ\).
Work out the bearing of \(A\) from \(B\). This is the angle marked \(x\).
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Calculator 2 marks
A coastguard at \(S\) can see a yacht at \(Y\) and a buoy at \(U\).
The bearing of \(Y\) from \(S\) is \(061^\circ\).
The bearing of \(U\) from \(S\) is \(152^\circ\).
Work out the size of the angle marked \(x\).
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Calculator 6 marks
Here is a map showing points \(P\) and \(Q\).
(a)Mateo wants to measure the bearing of \(P\) from \(Q\).
Mateo draws the line \(QP\) and a north line at \(Q\), then measures the angle clockwise from the north line to the line \(QP\). The angle is \(85^\circ\).
Mateo says that the bearing of \(P\) from \(Q\) is \(085^\circ\).
Is Mateo's method correct? Give a reason for your answer.
(b)On a different map, the bearing of \(D\) from \(C\) is \(315^\circ\).
Yara says, "\(D\) is south east of \(C\)."
Is Yara correct? Give a reason for your answer.
(c)A map of an island is drawn on a grid of squares of side \(2\) cm. An airport, \(E\), is marked on the map.
Scale: \(1\) cm represents \(14\) km.
A plane flies due south from the airport. On the map the coast is \(5\) squares due south of \(E\).
How far does the plane fly until it reaches the sea?
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Calculator 2 marks
A helicopter travels in a straight line from the hospital to the island on a bearing of \(117^\circ\).
It then travels straight back from the island to the hospital.
Calculate the bearing of the return journey.
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Calculator 2 marks
Yusuf cycles from \(A\) to \(B\) on a bearing of \(319^\circ\).
At \(B\) he turns \(90^\circ\) anticlockwise and carries straight on.
Find the bearing he is cycling on now.
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Calculator 4 marks
A ferry sails from \(P\) to \(Q\) on a bearing of \(080^\circ\).
It then sails from \(Q\) to \(R\) on a bearing of \(146^\circ\).
(a)Find the size of angle \(PQR\), marked \(x\) on the diagram.
(b)Find the angle it turns through at \(Q\).
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Calculator 3 marks
The diagram shows the route of a yacht. It sails from \(A\) to \(B\), and then from \(B\) to \(C\).
The bearing of \(B\) from \(A\) is \(058^\circ\), and angle \(ABC = 102^\circ\).
Calculate the bearing of \(C\) from \(B\).
- \(270^\circ\)
- south
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(a) Monument
(b) 180°
(c) \(544\ \text{m}\)
(d) The answer to part (c) is the straight-line distance, but a walk has to follow roads and paths, which cannot go in a straight line between the two places, so the route is longer. - \(307^\circ\)
- \(91^\circ\)
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(a) Yes: a bearing of P from Q is measured clockwise from the north line at Q, and that is what Mateo did
(b) No: a bearing of 315° points north west
(c) \(140\ \text{km}\) - \(297^\circ\)
- \(229^\circ\)
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(a) \(114^\circ\)
(b) \(66^\circ\) - \(136^\circ\)
Takes a couple of seconds the first time a sheet is made.