angle of elevation and depression

Chapter 10-Angle of Elevation and Depression

MATHEMATICS DEPARTMENTSEK MEN KEB LOKMAN HAKIM

81900, KOTA TINGGI

CHAPTER 10ANGLES OF ELEVATION AND

DEPRESSION

PREPARED BYMR ZAIDI NORLI B M NOAR

SMK LOKMAN HAKIM81900 KOTATINGGI

Guru Cemerlang, KPM

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ANGLE OF ELEVATION

1. By drawing a horizontal line and a line of sight, identify the angle of elevation of P from R, of the following diagram.

a) b)

c) d)

e) f)

g) h)

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P

Q S

R

Q S

R

P

Q S

R

P

QS

R

P

QSR

P

QS

R

P

Q S

R

P

QS

R

P


2. In diagram PQ and RS are two vertical poles on a horizontal plane. Calculate the angle of elevation of P from point R.

a) b)

c) d)

e) f)

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P

Q S

R10m

4m

20m

P

Q S

R12m

8m

15m

P

Q SR20m 5m14m

P

QS

R

3m

18m

20m

4m

P

QS

R24m

30m

P

Q S

R10m

5m

20m

PQ SR

20m 6m30m


g) h)

3. In diagram, PQ and RS are two vertical poles on a horizontal plane. Calculate the value of h.

a) angle of elevation = 42 b) angle of elevation = 38

c) angle of elevation of P from R = 24 d) angle of elevation of P from R = 53

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3m

P

QS

R9m

16m

P

Q S

R4m

10m

2m

P

QS

R

8m

P

Q S

R12m

20m

18m

P

QS

R

10m

h m

h m h m

h m


e) angle of elevation of P from R = 63 f) angle of elevation of P from R = 36

EXERCISE 1

1.

2.

3.

4.

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P

Q S

R16m

30m

5m

P

QS

R

15m

h m

h m

4m

R

QP

S

10m

In diagram PS and QR are two vertical poles on horizontal ground. The angle of elevation of R fro S is 28. Calculate, in m, the height of the vertical pole QR

5m

R

QP

S

8m

h m

In diagram PS and QR are two vertical poles on horizontal ground. The angle of elevation of R from S is 25. Calculate the value of h.

S

P Q

R6m

4 m

In diagram PS and QR are two vertical towers on a horizontal ground. The angle of elevation of S from R is 22. Calculate, in m, the distance PQ

S

P Q

R

20m 15 m

In diagram, PS and QR are two vertical poles on a horizontal plane. The angle of elevation of S from R is 15. Calculate, in m, the distance from R to S


5.

ANGLE OF DEPRESSION

1. By drawing a horizontal line and a line of sight, identify the angle of depression of R from P.

a) b)

c) d)

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F

D E

G10m

4.5 m

20m

In diagram, DF and EG are two vertical flagpoles on a horizontal plane. Calculate the angle of elevation of F from G

S

P

Q

R

S

P

QR

S

P

Q

R

S

P

Q

R

SPQR


e) f)

g) h)

2. The diagram shows two vertical poles PQ and RS, on a horizontal plane. Calculate the angle of depression of R from point P.

a) b)

c) d)

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S

P

Q

R

S

P

Q

R

S

P

Q

R

P

Q S

R

4m8m

10m

P

QS

R10m

20m

Q S

R

2m

10m

20m

P

P

QS

R15m

10m

3m

6m


e) f)

3. In diagram, PQ and RS are two vertical poles on a horizontal plane. Calculate the value of h, in m.

a) the angle of depression of R from P = 20

b) the angle of depression of R from P = 40

c) the angle of depression of R from P = 50

d) the angle of depression of R from P = 32

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P

QS

R

6m

20m

20m

Q S

R

5m20m

10m

P

Q S

R8m

10m

P

h m

Q S

R18m

20m

P

h m

P

QS

R

4m

12m

h m

P

QS

R20m

12m

h m


e) the angle of depression of R from P = 70

f) the angle of depression of R from P = 62

EXERCISE 2

1.

2.

3.

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Q S

R25m

25m

P

h m

P

QS

R

6m

18m

h m

P Q

R5m

8m

S In diagram, PS and QR are two vertical poles on a horizontal plane. The angle of depression of R from S is 20. Calculate in m, the height of the pole QR

R

QP

S

5m7m

In diagram PS and QR are two vertical poles on horizontal plane. Calculate the angle of depression of S from R

Q R

S

5m

10m

P In diagram, PQ and RS are two vertical poles. The angle of depression of S from P is 25. Calculate the height in m, of the pole PQ


4.

5.

OBJECTIVE QUESTION

1.

2.

3.

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P Q

30m

TIn diagram, PT is a tower. The angle of depression of Q from T is . Calculate the distance of PQ

D E10m

F

G

3m

In diagram EFG is a vertical wall. The angle of depression of D from G is 40. Calculate, in m, the length of FG

160°

P Q S T

R In the diagram, PQST is a straight line. The angle of depression of Q from R isA 20 C 60B 30 D 70

E

F V

U4m

In the diagram, EF and UV are two vertical poles. The angle of elevation of U from F is 32° while the angle of depression of U from E is 28°. Calculate the height of the pole EF in m, correct to one decimal place.A 5.4 C 7.4B 6.4 D 8.4

PR

h m2 m

In the diagram, PQ and RS are two vertical poles on a horizontal plane. The angle of elevation of R from P is 52°. Calculate the value of h.A 9. 4 C 17. 4B 11. 4 D 19. 2


4.

5.

6.

7.

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Q S12 m

X

Y N

L

KIn the diagram, XY and KLN are two vertical poles on a horizontal plane. The angle of elevation of K from X isA CB D

U

V Y

X

12 m

The diagram shows two vertical poles, UV and XY, on a horizontal ground. The angle of depression of vertex U from vertex X is 38. Calculate the angle of elevation of vertex U from YA 12° 25’ C 54° 18’B 35° 42’ D 77° 35’

Q

P

R S

T

The diagram shows two sticks planted vertically in the ground. PQ and PT are two ropes tied to the two sticks. The angle of elevation of Q from P isA CB D

H

E

F

The diagram shows the vertical side view of a chair on a horizontal floor. The angle of depression of I from F isA CB D


8.

9.

10.

11.

12.

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GI

P

Q

R S

20°

The diagram shows a vertical wooden structure PQRS erected on a horizontal ground. The angle of elevation of P from S is 50°. Find the angle of depression of S from Q.A 30 C 60B 40 D 70

E

P F Q

In the diagram, EF is an upright pole erected on a horizontal ground. FQ = 3 FP. Given that the angle of elevation of E from P is 68, find the angle of depression of Q from E isA 22° 18’ C 39° 31’B 31° 15’ D 42° 15’

P

Q

R S

1. 5m

●

●

●The diagram shows a vertical flag post PQ on a vertical wall. The angle of elevation of P from S on the horizontal ground is 75° and the angle of depression of S from Q is 43°. The length of PQ in m isA 1. 1 C 3. 7B 1. 2 D 4. 5

X

Y

U

V7 m

The diagram shows two vertical poles XY and UV erected on a horizontal ground. The angles of depression of U and V from X are 20° and 50° respectively. The length of pole UV in m isA 2. 08 C 4. 04B 2. 97 D 5. 79

K

L N

M

4 m

12 m

x m

In the diagram, KL and MN are two vertical poles standing on a horizontal a horizontal ground. The angle of elevation of M from K is 18°Calculate the value of x.A 7. 7 C 13. 8B 7. 9 D 15. 4


13.

14.

15.

16.

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P

R X W

VU●

70°

h m

The diagram shows a vertical pole PR tied to a rectangular block of wood by a rope UP. The angle of elevation of P from X is 30° and the height of the rectangular block of wood is 0. 2m. Calculate the value of h.A 0. 38 C 0. 48B 0. 45 D 0. 54

X

9 m

YSR● ●

The diagram shows a vertical pole XY standing on a horizontal ground. The angles of elevation of X from S and R differ by 15°. Given that the angle of elevation of X from S is 40°, calculate the distance of RS in m.A 8. 57 C 3. 36B 5. 14 D 2. 37

R

U

T P

SIn the diagram, RT and SP are two vertical poles on a horizontal plane. The angle of elevation of R from S isA CB D

E

F

R

S

V

W

7. 4m3 m

1 m2 m 2 m

The diagram shows a wall VW and two vertical poles EF and RS. The angle of depression of E from R is p° and the angle of depression of E from V is q°. the value of q – p isA 12 C 15B 13 D 16


17.

18.

19.

20.

21.

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X

Y

U

V10 m

In the diagram, XY and UV are two vertical poles. The length of pole XY is twice that of pole UV and the angle of depression of U from X is 35°. The length of pole XY in m isA 11. 5 C 16. 4B 14. 0 D 28. 0

E

R

F

S

12 m

15 m

In the diagram, ER and FS are two vertical lamp posts on a horizontal plane. The angle of depression of peak F from peak E is 17°. Calculate the height of poles FS.A 2. 34 C 7. 41B 5. 28 D 7. 61

U

V

P

Q18 m

12 m

In the diagram, UV and PQ are two vertical poles on a horizontal plane. The angle of depression of peak U from peak P is 26°. Calculate the height of pole UV in m.A 2. 49 C 4. 11B 3. 22 D 4. 18

K

L

M

N

8 m

The diagram shows two vertical flag posts, KL and MN, on a horizontal plane. The angle of elevation of vertex M from vertex K is 48°. Calculate the angle of depression of the foot N from the vertex K.A 12°33’ C 36° 10’B 23° 25’ D 48°23’

S

P Q

R

4 m

In the diagram, PS and QR are two vertical poles on horizontal ground. The angle of elevation of R from S is 28°. Calculate in m, the height of the vertical pole QR.A 5. 32 C 18. 81B 9. 32 D 22. 81


22.

23.

24.

25.

26.

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10 m

S

P

R

Q8 m

5 mIn the diagram, PS and QR are two vertical walls on horizontal ground. The angle of depression of R from S is 20°. Calculate, in m, the height of the wall QR.A 2. 09 C 7. 91B 2. 91 D 16. 98

S

P

R

Q

6 m8 m

In the diagram, PS and QR are two vertical towers on horizontal ground. The angle of elevation of S from R is 22°. Calculate in m, the distance PQ.A 0. 81 C 9. 90B 4. 95 D 14. 85

S

P

R

Q

20 m15 m

In the diagram, PS and QR are two vertical pillars on horizontal ground. The angle of elevation of S from R is 15°. Calculate in m, the distance from R to S.A 5. 78 C 18. 66B 11. 59 D 19. 32

S

P

R

Q

5 m

6 m

7 m

In the diagram, PS and QR are two television antennaes on horizontal ground. Calculate the angle of depression of S from R.A 15° C 19. 47°B 18. 43° D 70. 53°

S

P Q

R

5 m

8 m

h m

In the diagram, PS and QR are two vertical poles on horizontal ground. The angle of elevation of R from S is 25°. Calculate the value of h.A 3. 7 C 17. 2B 8. 7 D 22. 2


27.

28.

29.

30.

31.

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P

R S

TQ

In the diagram, PQR and ST are two vertical pillars. The angle of elevation of point P from point T isA CB D

P

Q R

S

10 m

5 m

In the diagram, PQ and RS are two vertical walls. The angle of depression of S from P is 25°. Calculate the height, in m, of the wall PQ.A 4. 66 C 9. 66B 7. 33 D 12. 33

T

P R

S5 m

2 m

In the diagram, PT and RS are two vertical poles on horizontal ground. The angle of elevation of T from S is 20°. Calculate, in m, the distance between the two poles PR.A 1. 09 C 5. 49B 1. 82 D 8. 24

D E

F

G

10 m

3 m

In the diagram, EFG is a vertical wall. The angle of depression of D from G is 40°. Calculate, in m, the length of FG.A 5. 39 C 8. 92B 8. 39 D 11. 39

P

A B

Q

3 m

h m

7 m

In the diagram, AP and BQ are two vertical pillars. The angle of elevation of Q from P is 22°. Calculate the value of h.A 2. 8 C 14. 3B 5. 8 D 17. 3


SUBJECTIVE QUESTIONS

1.

2.

3.

4.

5.

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P Q

R

20 m

In the diagram, QR is vertical pole. The angle of elevation of R from P is 25° 40’. Calculate the height of the pole.

T

P Q

30 m

In the diagram, PT is a tower. The angle of depression of Q from T is 20° 11’. Calculate the distance PQ.

PQ

R

30 m

In the diagram, QR is a vertical wall. The angle of elevation of R from P is 27° 12’. Calculate the height of the wall.

F

D E

G4. 5 m

20 m

10 mIn the diagram, PQ and RS are two vertical walls. The angle of depression of S from P is 25°. Calculate the height, in m, of the wall PQ.

H

G F40 m

In the diagram, GH is a vertical monument. The angle of elevation of H from F is 25° 18’. Calculate the height of the monument GH.


6.

7.

8.

9.

10.

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P

H K

Q

10 m

8 m

In the diagram, HP and KQ are two verticals pillars. The angle of elevation of Q from P is 26°34’. Calculate the height of the shorter pillar PH.

A B P

Q

80 m

In the diagram, PQ is a building 80 m tall. From Q, the angle of depression of two points, A and B are 25° and30° respectively. Calculate the distance between A and B.

M

P Q

N

8 m

10 m

In the diagram, PM and QN are two vertical towers. The angle of elevation of N from M is 40° 22’. Calculate the height of the taller tower QN.

P

A

Q

B

5 m7 m

In the diagram, AP and BQ are two vertical walls. The angle of elevation of Q from P is 11. 3°. Calculate the distance between the two walls, AB.

T

A B

5 m

In the diagram, BT is a vertical flag pole, 5 m tall. The angle of depression of A from T is 20°. Calculate the distance from A to T.


11.

12.

13.

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P

A

Q

B

10 m

12 m

In the diagram, AP and BQ are two vertical poles. The angle of elevation of Q from P is 26° 34’. Calculate the height of the shorter pole, AP.

Q

P

S

R100 m

In the diagram, PQ and RS are two buildings. The angle of depression of S from Q is 20°.Calculate the distance from Q to S.

P Q R

ST

5 m

In the diagram, QT and RS are lamp posts of the same height. From P, the angles of elevation of T and S are 40° 26’ and 25° 19’ respectively. Calculate (a) the height of the lamp post.

(b) the distance between the two lamp posts.

angle of elevation and depression

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