Cambridge International Mathematics

Trigonometry (Chapter 15) 331

EXERCISE 15E

1 Draw diagrams to represent bearings from O of:

a 136 o b 240 o c 051 o d 327 o

2 Find the bearing of Q from P if the bearing of P from Q is:

a 054 o b 113 o c 263 o d 304 o

3 A, B and C are the checkpoints of a triangular orienteering course. For each of the following courses,

find the bearing of:

i B from A ii C from B iii B from C

iv C from A v A from B vi A from C.

ab

4 A bushwalker walks 14 km east and then 9 km south. Find the bearing of his finishing position from

his starting point.

5 Runner A runs at 10 km/h due north. Runner B leaves the same spot and runs at 12 km/h due east.

Find the distance and bearing of runner B from runner A after 30 minutes.

6 A hiker walks in the direction 153 oand stops when she is 20 km south of her starting point. How far

did she walk?

7 A ship sails for 60 km on a bearing 040 o. How far east of its starting point is the ship?

8 Natasha is 50 m due east of Michelle. Natasha walks 20 m due north, and Michelle walks 10 m due

south. Find the distance and bearing of Michelle from Natasha now.

9 An aeroplane travels on a bearing of 295 oso that it is 200 km west of its starting point. How far has

it travelled on this bearing?

10

Right angled triangles occur frequently in 3 -dimensional figures. We can use Pythagoras’ theorem and

trigonometry to find unknown angles and lengths.

F 3-DIMENSIONAL PROBLEM SOLVING [8.7]

NN

C

N

A

B

41°

142°

279°

N

N

N

27°

151°

246°

B

A

C

A fishing trawler sails from port P in the direction 024 ofor

30 km, and then in the direction 114 ofor 20 km.

Calculate:

a the distance and bearing of the trawler from P

b the direction in which the trawler must sail in order to

return to P.

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Y:\HAESE\IGCSE01\IG01_15\331IGCSE01_15.CDR Tuesday, 7 October 2008 2:21:26 PM PETER