CHAPTER: 22
BEARING
Directions 22.1 Compass Directions
Nort North-w h-west est 315r
Nort North h 000r/360r Nort Northh-east east 045r
West 270r
East 090r
South-w outh-west est 225r
22.2
Th e
South outh 180r
Southouth-east east 135r
Be Bea aring ring
digit number number f rom Bearing is written as a three dig rom 000r to 360r. The The b earing of point point Q f rom rom point P is t he angle b etw etween the north north direction direction through rough P and and the line PQ, measured clockwis ckwise direction. measured in a clo irection.
b) b)
a)
Nort North h
Nort North h
60r 60r
Q
The The b earing of Q f rom rom P = 060r
130r
Q
P
P
The The bearing of Q f rom rom P = 130r
c) d) Nort North h
250r
The The b earing of Q f rom rom P = 250r
Nort North h
Q
P
P
300r
Q
The The bearing of Q f rom rom P =300r
Bearing
1
P f rom To f ind ind the bearing of P rom Q, given that the b earing of Q f rom rom P is Ur,
Bearing of Q f rom rom P
P f rom Bearing of P rom Q
U R ange ange value of U
N
0r U < 180r
U
P
N
U Q U + 180r
N N
P
180r U 360r
U
U
U - 180r Q
Exam Exam ple ple 1 ( State State the b earing of point point A f rom rom point B based ased on the given inf inf ormation ormation ) a) Point K , L and and M are on level ground. ground. Fin Find d the bearing of i) K f rom rom N . ii) M f rom rom K . North
North
M
115r
K
60r 60r N Solution
i)
ii)
North
North M
North
115r 115r
K
60r 60r
K
60r 60r
115r 115r
N
Bearing of K f rom rom N = 060r
180r 180r
Bearing of M f rom rom K = 115r + 180r = 295r
Bearing
2
R
b) b)
P . Fin P f rom In a diagram, iagram, R is due north north of P F ind d the bearing of P rom Q.
100r
P 30r
Q
Solution
North
N PQ ( or R PQ ) = 50r The The b earing of Q f rom rom P = 050r
R
P f rom The The b earing of P rom Q = 50r + 180r = 230r
100r 100r P
50r 50r 30r 30r
Q
50r 50r 180r 180r
Exam Exam ple ple 2 ( solve pro blem blem ) a) ( Wit With h a diagram ) P
In the diagram, iagram, points P , Q and and R are on horizontal ground. ground. PQ R is an isosceles triangle. triangle. Given Given that P R = Q R and and P is due north north of Q, f ind ind the b earing of i) R i) R f rom rom Q ii) P f rom R rom R
110r
Q
R Solution
P
North
i) PQ R = 35r The The bearing of R R f rom rom Q = 035r
35r North
Q
35r
110r
35r
P f rom R ii) The The b earing of P rom R = 360r - 35r = 325r
R
Bearing
3
b) b) ( Wit With hout a diagram ) The The b earing of Q f rom rom P is 150r and and R is due west of Q. Given Given that PQ = P R = 30 m. Calculate Calculate the bearing bearing of i) P f rom R rom R ii) R ii) R f rom rom P Solution
(1) (1) Sk etch etch a diagram
North
P
R
150r
Q
(2) (2) Answer the question(s) based on your sk etch. etch. North
(i)
150r
North
(ii)
150r P
150r
P
30r R
R
P f rom R The The bearing of P rom R = 030r
The The b earing of R R f rom rom P = 360r - 150r = 210r
2) Questions tions Base ase On On Exam Examiinati nation on Format mat North
1)
In the diagram, iagram, D is due north north of E and and F is due southsouth-east east of E .
North
D
N
68r M E
In t he diagram, iagram, f ind ind the b earing of M f rom rom N . A. B. C. D.
The The bearing of F f rom rom E F is A. B. C. D.
068r 136r 248r 280r
Bearing
045r 090r 135r 180r
4
3)
In the diagram, iagram, points p oints P , Q and and R are on horizontal ground. ground. The The bearing of R R f rom rom P is North
6)
North
A 140r 60r B
110r P
C
40r
The The b earing of B B f rom rom C is C is
A. B. C. D.
4)
110r 250r 280r 300r
North
M
A. B. C. D.
Q
R
7)
Nort
R P
North
115r 55r
K
In the diagram, iagram, points p oints P , Q and and R are on the horizontal ground. ground. R R is due north north of P . The The bearing of Q f rom R rom R is 148r. The Th e P f rom bearing bearing of P rom Q is
N
In the diagram, iagram, points K , M and and N are on level ground. ground. Fin Find d the bearing of K f rom rom N . A. B. C. D.
120r 160r 260r 270r
010r 040r 060r 065r
A. B. C. D.
032r 116r 148r 212r
8)
North T
North
5)
R P S
80r
R
The The b earing of R R f rom rom P is
In the diagram, iagram, T is due north north of S . The The bearing bearing of T f rom R rom R is 025r and and bearing b earing R f rom rom S is 250r. The The bearing of S f rom rom R is
A. B. C. D.
A. B. C. D.
Q
48r
038r 047r 052r 125r
Bearing
060r 065r 070r 075r
5
9) A. B. C. D.
P
North
M
N
56r
078r 242r 282r 294r R
13) 13) In the diagram a bove bove,, points M , N and and P are on the horizontal level. level. The The bearing P f rom of P rom M is 062r. Bearing M and and N is A. B. C. D. 10) 10)
P 50r Q
152r 208r 298r 302r
In the diagram, iagram, P, Q and and R are on the horizontal ground. ground. Given Given that the bearing of point p oint R f rom rom point Q is 030r and and the bearing bearing of point P f rom rom Q is 300r. Find ind the b earing of point point P f rom rom R.
Points K , L and and M are on the horizontal plane plane.. L is due east of K . The Th e b earing of M f rom rom K is K is 070r and and bearing b earing of L f rom rom M is 140r. Fin Find d KML. A. B. C. D.
110r 120r 130r 140r
A. B. C. D.
040r 220r 240r 250r
14) 14) P
82r 11) 11)
Q H
R 28r In the diagram, iagram, Q is due east of R and and the b earing of P f rom rom R is 030r. The The bearing bearing of P f rom rom Q is
120r F
G
A. B. C. D.
In the diagram, iagram, G is due east of F. The The bearing bearing of H f rom rom G is A. B. C. D.
202r 212r 302r 312r
128r 218r 308r 318r P
15) 15)
R
Q Y
12) 12) Z
In the diagram, iagram, R is due east of P and an d Q is due south south of P. The The bearing of R f rom rom Q is 080r. The The bearing of Q f rom rom R is R is
40r X
In the diagram, iagram, poits X, Y and and Z are on the horizontal plane. lane. Y is due north north of X and and the bearing of Y f rom rom Z is 062r.
Bearing
A. B. C. D.
010r 090r 100r 260r 6
19) 19)
North
16) 16)
G
N
F
M
60r
2 r
In the diagram, iagram, L is due south south of N. The The bearing bearing of M f rom rom L is A. B. C. D.
E
H
L
In the diagram, iagram, E, F, G and and H are on the horizontal ground. ground. EFG is a straigh straight line and and HE = HF = FG. Fin F ind d the bearing of H f rom rom G.
080r 100r 240r 260r
A. B. C. D.
17) 17)
022.5r 045r 135r 202.5r
North
20) 20)
F
N
rth
F
r E
E
G In the diagram a bove bove,, P, E, F and and G are on the horizontal plane. lane. E is due north north of P and and the bearing of G f rom rom P is 134r. Find ind the bearing bearing of P f rom rom G.
In the diagram, iagram, E, F and and G are on the level ground. ground. EFG is an isosceles. isosceles. Find ind the b earing of G f rom rom F. A. B. C. D.
015r 105r 205r 255r
A. B. C. D.
18) 18)
046r 104r 224r 314r
North
ast Past
Yea Year SPM Questions. tions.
Nov 2003, Q14
P 250r
R E
1.
Q
50r
In the diagram, iagram, P, Q and an d R are on the horizontal ground. ground. PQ = QR . The The bearing bearing of R f rom rom P is 250r and and the bearing bearing of Q f rom rom P is 160r. Find ind the bearing bearing of Q f rom rom R. A. B. C. D.
G
2 r F
In the diagram, iagram, E lies to the north nort h of G. The The bearing bearing of G f rom rom F is
045r 070r 115r 330r
A. B. C. D. Bearing
110r 250r 290r 310r 7
July
2004, Q18
In the a bove b ove diagram shows the position of points points P and and Q. Fin Find d the bearing of point p oint P f rom rom point Q.
and R 2. Diagram 11 shows three p oints P, Q and whic which h f orms orms an equilateral triangle on a horizontal plane. lane.
A. B. C. D. July
The The point P is due north north of the p oint Q. The The bearing bearing of t f the p oint Q f rom rom the point R is R is o A. 060 o B. 120 C. 240o D. 300o
035r 055r 125r 215r
2005, Q17
oints, K, L and and M 5. Diagram 9 s hows three points, on a horizontal plane. lane.
Nov 2004, Q18
and R lie R lie on a horizontal plane. lane. P 3. Points P, Q and
o
The The b earing of L f rom rom K is 250 o LKM = 120 . Find ind the bearing of M f rom rom K. o A. 040 o B. 050 o C. 130 D. 140o
is due south south of Q. The The bearing of R f rom rom Q is 150r and and the b earing of P f rom rom R is 300r. Whic Which h of the f ollow ollowing diagrams shows the position position of P, Q and and R? A.
C.
North
Q
North
Nov 2006, Q17
Q
and N lie on a horizontal plane. lane. 6. Points M and
R
o
The The b earing of M f rom rom N is 060 . Whic Wh ich h of the f ollow ollowing diagrams shows the positions of M and and N?
P
P
B.
R D.
North
A.
North
B. .
P
P
R Q
Q
R
Nov 2005, Q16 North
4.
C.
D.
North
145r
P
Q
and and
Bearing
8
Nov 2007, Q16 7. Diagram Diagram 10 shows three points, oints, P,Q and and R, on a horizontal plane. lane.
R
Q
Nov 2008, Q17 9. Diagram Diagram 10 shows three points, oints, P,Q and and R, on a horizontal plane. lane.
0
26
P
P
0
38 It is given that Q lies due north north of P and and the bearing bearing of R f rom rom Q is 0750. Find ind the bearing of P f rom rom R. A. 049o o B. 101 C. 229o o D. 281 Jun
R
Q
It is given that P is due north north of Q. Fin Find d the bearing bearing of R f rom rom P. o A. 052 o B. 076 o C. 104 o D. 128
2007, Q18 Jun
8. In In Diagram 11, P,Q and and R are R are three p oints on a horizontal plane such such that PR=RQ=QP.
R
2008, Q17
10. Points Points P and and Q lie on a horizontal plane. lane. The Th e o bearing bearing of P f rom rom Q is 220 . Whic Which h diagrams shows the locations of P and and Q?
Nort North h
A.
B.
Nort North h
.
P
Q
2200
Q
0
220
Q
P Given that Q is due east of P, Fin Find d the bearing of Q f rom rom R. o A. 330 B. 150o C. 120o o D. 060
P Nort North h
C.
D.
Nort North h
P P
0
220
0
220
Q
Q
Bearing
9
ANSWERS Chapter ap ter 22 Bea Bearing ring
22.3
22.4
Questions tions Acco According rding to Exam Examiinati nation on Format mat 1. D 2.C 3.B 3.B 4. C 5. D 6.D 7. D 8. C 9. C 10. A 11. C 12. C 13. D 14. C 15. D 16. D 17. D 18. C 19. C 20. D 21. D SPM Past ast Yea Year Qu Questions tions
1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 10)
C C C D C A C B B A
Bearing
10
