chapter 16 i angles of ele & depression enrich
Post on 06-Apr-2018
226 Views
Preview:
TRANSCRIPT
-
8/3/2019 Chapter 16 I Angles of Ele & Depression ENRICH
1/14
Chapter 16: ANGLES OF ELEVATION AND DEPRESSION
16.1 Important concepts
16.1.1 ANGLE OF ELEVATION
The angle of elevation of a pointA from a lower point O is the acute angle measured up from thehorizontal line through point O to the line of sight, OA.
16.1.2 ANGLE OF DEPRESSION
The angle of depression of a pointB from a higher point O to the line of sight, OB
Angles of Elevation and Depression 128
O
A
Angle of elevation
Horizontal line
Angle of depression
Horizontal lineo
B
-
8/3/2019 Chapter 16 I Angles of Ele & Depression ENRICH
2/14
Questions According to Examination Format
P Q
T
1. In the diagram, TQ is a vertical flagpolestanding on a horizontal ground. Given
thatPQ = 20 m and TQ = 6 m, the angle
of elevation of T and P is
A 16.70 C 72.50
B 17.50 D 73.30
55 m
100 m
2. Based on the diagram, find the angle of
depression of the ball from the top of thebuilding.
A 24.20 C 61.20
B 28.80 D 65.80
E F30 m
3. In the diagram, the angle of elevation of
the top of the tree fromF is 220. The
height of the tree in metres is
A 11.24 C 21.08B 12.12 D 27.82
Q
R
P
h
6.2 m
4. In the diagram, angle of depression of
pointP from pointR is 150. Find the
value of h
A 16.6 m C 21.5 m
B 18.9 m D 23.1 m
S
P RQ5 m 2 m
5. In the diagram, SQ is a vertical polestanding on a horizontal ground. Giventhat the angle of elevation of S from P
is 300, find the angle of elevation of S
from R
A 130 C 55017
B 34043 D 770
P
Q 16 m
R
S
2 m
6. In the diagram,PQ andRS are twovertical poles standing on a horizontalground. Given that the angle of
depression ofR from P is 100, the
height of PQ in metres is
A 3.96 C 4.82
B 4.69 D 4.98
Angles of Elevation and Depression 129
-
8/3/2019 Chapter 16 I Angles of Ele & Depression ENRICH
3/14
M
N
U
V
2.5 m
4.8 m
7. In the diagram, MN and UV are two
vertical poles standing on a horizontal
ground. Given that the angle of
depression of M from U is 19.50NV
in metres is
A 6.2 C 7.1
B 6.5 D 7.3
E
F
G
P
9 m
8 m
10 m
8. In the diagram, E, Fand G are three
points on a horizontal ground. PE is a
vertical poleand the angle of elevation ofP from F is 15.50. Find the angle ofdepression of G from P
A 12.50
C 14.50
B 13.80 D 14.80
R
S
P
Q
6 m
3.3 m
T
9. In the diagram,PQ and TS are twovertical poles on a horizontal plane QRS.
Given that the angle of elevation of P
from R is 380, the angle of elevation ofP from T is
A 18.20 C 19.40
B 18.80 D 19.80
P
E
Q
F
R
G
2 m4.2 m
3.8 m
10.
100R from E
280Q from G
220P from F
Value of angleAngle of e levation of...
In the diagram,E, F and G are three points ona horizontal ground. PE, QF and RG arethree vertical poles. Based on the
information in the table, calculate the
perimeter of the triangle EFG
A 25.8 m C 27.6 m
B 26.7 m D 28.6 m
Angles of Elevation and Depression 130
-
8/3/2019 Chapter 16 I Angles of Ele & Depression ENRICH
4/14
R
P Q
15 m
11. In the diagram, QR is a vertical pole
on a horizontal ground. The angle of
elevation ofR from P is 280.Calculate the height, in m, of the pole
QRA 7.04 C 13.24
B 7.98 D 28.21
R
PQ
6 m
12. In the diagram,PR is a vertical wall 6m
high. The angle of depression of Q
from R is 250. Calculate the distance, inm, from P to Q
A 2.80 C 12.87
B 8.57 D 22.39
10 m
N
ML
13. In the diagram, MN represents a towerstanding on horizontal ground. The
angle of depression ofL from N is
520. Calculate the height, in m, of thetowerMNA 7.88 C 12.80
B 9.00 D 18.81
P Q
R
S
25 m
18 m
14. In the diagram, QRS represents avertical wall of height 18 m. The angle
of elevation of R fromPis 260.
Calculate the height, in m, from R to S
A 4.47 C 6.81
B 5.81 D 12.19
S
R
PQ20 m15. In the diagram, QRS represents a
building. The angle of elevation ofR
from P is 200 while the angle of
depression ofP from S is 300. Calculate
the distance, in m, from R to SA 3.53 C 18.83
B 4.27 D 27.36
Q
P
S
R
5 m8 m
16. In the diagram,PQ and RS are twovertical poles. The angle of elevation
of Q fromR is 220. Calculate thedistance PR in metres
A 8.60 C 10.88B 12.38 D 22.90
Angles of Elevation and Depression 131
-
8/3/2019 Chapter 16 I Angles of Ele & Depression ENRICH
5/14
T
P Q R
S
10 m
4 m
17. In the diagram, P, Q and R are three
points on horizontal ground. PT and RS
are two vertical poles. The angle of
elevation of T from Q is 450 whereas
the angle of depression of Q from S is
35
0
. Find the distance, in m, between thetwo poles
A 8.19 C 11.00
B 9.74 D 12.19
18. A man, 1.7 m tall, is standing 20 m from a
monument. The angle of elevation of the top
of the monument from the eyes of the man is
230. The height, in m, of the monument is
A 8.49 C 10.19
B 10.03 D 45.42
P
Q R S
20 m
5 m
19. In the diagram,PQ is a vertical pole.
The angle of elevation ofP from S is
450. Calculate the angle of depressionof R from P
A 1402 C 41025
B 360
52 D 530
8
S
P QR
10m
4 m
20. In the diagram,PS is a vertical pillar.
The angle of depression ofR from S is
200. Calculate the distance, in m, fromQ to R
A 5.40 C 7.64
B 7.42 D 9.40
Angles of Elevation and Depression 132
-
8/3/2019 Chapter 16 I Angles of Ele & Depression ENRICH
6/14
SPM Past Year Questions
SPM 2003
1. In Diagram, TS and UV are two vertical poles standing on horizontal ground. The angle of
elevation of V from S is .420
VS
3 m h m
T U
Calculate the value of h.
A 10.4 C 14.1
B 12.0 D 17.9
SPM 2004 (July)
2. In Diagram , S, M and T arecollinear points on a horizontal plane. SM = MT and TU is avertical pole.
A wire is tied from the vertex U to the point S. Calculate the angle of elevation of vertex U
from the the point M
A 22037
B 50
012
C 39048
D 67023
Angles of Elevation and Depression
U
TS
M
25 m10 m
DIAGRAM 10
133
-
8/3/2019 Chapter 16 I Angles of Ele & Depression ENRICH
7/14
SPM 2004
In Diagram , MN and PQR are two vertical poles on a horizontal plane.
P
M Q
N R
The angle of elevation of point P from point M is
A MPQ C PMR
B PMQ D PNR
4. In Diagram, PQ and RS are two vertical poles on a horizontal plane.R
P 25 m
Q 20 m S
The angle of depression of peak P from peak R is 34 0 . Calculate the
height, in m, of the pole PQ.
A 4.65 C 11.51
B 8.42 D 13.82
SPM 2005 (July)
5. Diagra
m 17
shows twoflats
adjacent to
each other
on ahorizontal
plane.Fourfriends are
seating at balconiesP, Q, R and T respectively.
Which of the following is the angle of elevation of P from R?
A PRQ B PRC RPQ D RTP
Angles of Elevation and Depression
P
Q
T
R
JEBAT
BLOCKTUAH
BLOCK
DIAGRAM 17
134
-
8/3/2019 Chapter 16 I Angles of Ele & Depression ENRICH
8/14
6. In Diagram 8,J, K, L and Mare four points on a horizontal ground. MN is a vertical pole
with the height of 20 m,JM = ML JKL= 900
Calculate the angle ofelevation of vertexN from the point L
A 66025
B 26
034
C 33041
D 21048
SPM 2005
7. Diagram below shows two vertical poles, PS and QR, on a horizontal plane.
P
Q25 m
S R
The angle of depression of vertex Q from vertex P is 42 0 . Calculate the angle of elevation of
vertex Q from S.
A 32 0 C 57 0 59 '
B 41 0 59 ' D 68 0 11 '
Angles of Elevation and Depression
N
MJ L
K
80 m 60 m
DIAGRAM 8
135
10 m
-
8/3/2019 Chapter 16 I Angles of Ele & Depression ENRICH
9/14
SPM Year 2006 (July)
8. Diagram below shows the position of a rescuer and the position of an occupant who is trapped
on the 3rd floor of a tower.
Tower
Occupant
Rescuer 12 m
Te angle of elevation of the occupant from the rescuer is 35. Calculate the distance, in m, of the
rescuer from the bottom of the tower.
A 14.85 C 18.13
B 17.14 D 20.92
SPM Year 2006 (November)
9. In Diagram below , PQ and TR are two vertical poles on a horizontal plane. S is a point on TR
such that PQ = SR .
The angle depression of P from T is
A TPS C PTS
B RPT D QTS
Angles of Elevation and Depression 136
Q
P
R
S Q
T
-
8/3/2019 Chapter 16 I Angles of Ele & Depression ENRICH
10/14
SPM Year 2006 (November)
10. In diagram, JK is a vertical flag pole. KL is horizontal.
The angle of elevation of J from L is 420. The height, in m, of the flag pole is
A. 23.42 C. 31.51
B. 26.01 D. 38.87
SPM Year 2007 (June)
11. Diagram 10 shows two towers on a horizontal plane.
P and Q are two points on the top of the towers as shown. R is a point vertically below Q.
The angle of elevation of Q from P is 55 and the angle of elevation of R from P is 40 .Calculate the distance, in m,from Q to R,
A. 35.34 C. 29.50
B. 15.53 D. 10.58
Angles of Elevation and Depression 137
35m LK
J
60cm
P
Q
R
Digram 10
-
8/3/2019 Chapter 16 I Angles of Ele & Depression ENRICH
11/14
SPM Year 2007 (November)
12 . In diagram 9, PQ and RS are two vertical poles on a horizontal plane. The height of RS is
twice the height of PQ. The angle of depression of P from vertex R is 530 .
Calculate the height, in m, of RS.
A. 15.07 C. 30.14
B. 26.54 D. 53.08
SPM Year 2008 (June)
13 In Diagram 9 Q and S are two points on a horizontal plane . R is the top of a vertical
flagpole
SR
The angle of elevation of R from Q is 52o. The distance between Q and S is 14 m.
Calculate the height, in m, of flagpole SR
A. 10.94
B. 11.03
C. 15.59
Angles of Elevation and Depression 138
Q S
R
Diagram 9
P
Q
R
S20m
Diagram 9
-
8/3/2019 Chapter 16 I Angles of Ele & Depression ENRICH
12/14
D. 17.92
SPM Year 2008 November (Q 15)
14. Diagram 8 shows two vertical flagpoles on a horizontal plane P,Q,R,S and T are five pointson the poles such that QR = ST
Name the angle of elevation of point P from point S
A. QSP
B. QPS
C. RSP
D. RTP
SPM Year 2008 November (Q16)
15. Diagram 9 shows a tower PQ . The point P,R and S lie on a horizontal plane
The angle of depression of R from Q is 45o. Find the angle of elevation of Q from S.
A. 22o 37
B. 35 o13
C. 54 o47
Angles of Elevation and Depression 139
12m
5m
Q
P R
SDiagram 9
P
Q
R
S
T
Diagram 8
-
8/3/2019 Chapter 16 I Angles of Ele & Depression ENRICH
13/14
D. 67 o23
ANSWERS
Chapter 16: Angles of Elevation and Depression
16.1.1
a) i. Line of sight
ii Angle of elevation
iii.Horizontal line
b) i. Line of sight
ii Angle of elevation
iii.Horizontal line
c) i. Line of sight
ii Angle of elevation
iii.Horizontal line
16.1.2
a) i. Horizontal line
ii Angle of depression
iii.Line of sight
b) Horizontal line
ii Angle of depression
iii.Line of sight
c) Horizontal line
ii Angle of depression
iii.Line of sight
16.2.1(a) i. JK
ii. JK
iii. JM
(b) i. QS
ii. PS
iii. RS
(c) i. EG
ii. EF
iii. EH
16.2.2
(a)
520
18 m
(b)
3238
10 m 10 m
1.57 m
0 0
(c) (d)
Angles of Elevation and Depression 140
-
8/3/2019 Chapter 16 I Angles of Ele & Depression ENRICH
14/14
1.55m
360 John
Hassan
Ganesh11.5 m
38
490
0
16.2.3
(a) = 8.590(b) 8.88 m
(c) 14.9 m
(d) (i) 7.43 m (ii) 15.10
(e) (i) 8.530 (ii) 4.94 m
(f) (i) 49.52 m (ii) 35.08 m
Questions According to Examination
Format
1. A
2. C
3. B
4. D
5. C
6. C
7. B
8. A
9. C
10. D
11. B
12. C
13. C
14. B15. B
16. B
17. D18. C
19. D
20. A
Past Year Questions
1. B
2. B3. B
4. C
5. A6. D
7. C
8. B9. A
10. C
11. A
12. D13.D
14. A
15.C
Angles of Elevation and Depression 141
top related