chapter 16 i angles of ele & depression enrich

8/3/2019 Chapter 16 I Angles of Ele & Depression ENRICH

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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


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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



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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



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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



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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



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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


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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


P

Q

T

R

JEBAT

BLOCKTUAH

BLOCK

DIAGRAM 17

134


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 '


N

MJ L

K

80 m 60 m

DIAGRAM 8

135

10 m


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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


Q

P

R

S Q

T


10/14


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


35m LK

J

60cm

P

Q

R

Digram 10


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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


Q S

R

Diagram 9

P

Q

R

S20m

Diagram 9


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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


12m

5m

Q

P R

SDiagram 9

P

Q

R

S

T

Diagram 8


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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


iii.Horizontal line

c) i. Line of sight


iii.Horizontal line

16.1.2

a) i. Horizontal line

ii Angle of depression

iii.Line of sight

b) Horizontal line


iii.Line of sight

c) Horizontal line


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)



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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


chapter 16 i angles of ele & depression enrich

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