Chapter 16: ANGLES OF ELEVATION AND DEPRESSION 16.1 Important concepts 16.1.1 ANGLE OF ELEVATION The angle of elevation of a point A from a lower point O is the acute angle measured up from the horizontal line through point O to the line of sight, OA.

A

O

Angle of elevation Horizontal line

16.1.2 ANGLE OF DEPRESSION The angle of depression of a point B from a higher point O to the line of sight, OB

o

Horizontal line Angle of depression

B

Angles of Elevation and Depression

128

Questions According to Examination Format

T 100 m

P

Q

1. In the diagram, TQ is a vertical flagpole standing on a horizontal ground. Given that PQ = 20 m and TQ = 6 m, the angle of elevation of T and P is A B

16.70 17.50

55 m

2. Based on the diagram, find the angle of depression of the ball from the top of the building. A B

C 72.50 D 73.30

24.20 28.80

C 61.20 D 65.8

0

R 6.2 m P

Q

F

30 m

E

h

3. In the diagram, the angle of elevation of the top of the tree from F is 220. The height of the tree in metres is A 11.24 B 12.12

4. In the diagram, angle of depression of point P from point R is 150. Find the value of h

C 21.08 D 27.82

S

A B

16.6 m 18.9 m

C 21.5 m D 23.1 m

P R 2m

5m

P

Q

2m

R

5. In the diagram, SQ is a vertical pole standing on a horizontal ground. Given that the angle of elevation of S from P is 300, find the angle of elevation of S from R A B

130 340 43â&#x20AC;&#x2122;

Angles of Elevation and Depression

C 55017â&#x20AC;&#x2122; D 770

Q

16 m

S

6. In the diagram, PQ and RS are two vertical poles standing on a horizontal ground. Given that the angle of depression of R from P is 100, the height of PQ in metres is A B

129

3.96 4.69

C 4.82 D 4.98

U M

P

4.8 m

E

2.5 m N

V

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 19.50 NV in metres is A B

6.2 6.5

C 7.1 D 7.3

10 m G

8m F

9m

8. In the diagram, E, F and G are three points on a horizontal ground. PE is a vertical pole and the angle of elevation of P from F is 15.50. Find the angle of depression of G from P 12.50 13.80

A B

C 14.50 D 14.8

0

Q

P

R

6m Q

4.2 m F

T 3.3 m S

2m G

P 3.8 m

R

E

9. In the diagram, PQ and TS are two vertical poles on a horizontal plane QRS. Given that the angle of elevation of P from R is 380 , the angle of elevation of P from T is A B

18.20 18.80

C 19.40 D 19.8

0

10. Angle of elevation of... P from F Q from G R from E

In the diagram, E, F and G are three points on a horizontal ground. PE, QF and RG are three vertical poles. Based on the information in the table, calculate the perimeter of the triangle EFG A B

Angles of Elevation and Depression

Value of angle 22 0 28 0 10 0

130

25.8 m 26.7 m

C 27.6 m D 28.6 m

R

R

6m P

Q

15 m

11. In the diagram, QR is a vertical pole on a horizontal ground. The angle of elevation of R from P is 280. Calculate the height, in m, of the pole QR A B

7.04 7.98

Q

P

12. In the diagram, PR is a vertical wall 6m high. The angle of depression of Q from R is 250. Calculate the distance, in m, from P to Q A B

C 13.24 D 28.21

2.80 8.57

C 12.87 D 22.39

S

N

R 18 m

L

M

10 m

P

13. In the diagram, MN represents a tower standing on horizontal ground. The angle of depression of L from N is 520. Calculate the height, in m, of the tower MN A

7.88 B 9.00

25 m

14. In the diagram, QRS represents a vertical wall of height 18 m. The angle of elevation of R from P is 260. Calculate the height, in m, from R to S A B

C 12.80 D 18.81

4.47 5.81

Q

R

5m P

P 20 m Q 15. In the diagram, QRS represents a building. The angle of elevation of R from P is 200 while the angle of depression of P from S is 300. Calculate the distance, in m, from R to S 3.53 4.27

Angles of Elevation and Depression

C 6.81 D 12.19

S

S

A B

Q

8m R

16. In the diagram, PQ and RS are two vertical poles. The angle of elevation of Q from R is 220. Calculate the distance PR in metres A 8.60 B 12.38

C 18.83 D 27.36

131

C 10.88 D 22.90

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

S T 10 m

A B

4m P

Q

8.49 10.03

C 10.19 D 45.42

R

17. In the diagram, P , Q and R are three points on horizontal ground. PT and RS are two vertical poles. The angle of 0 elevation of T from Q is 45 whereas the angle of depression of Q from S is 0 35 . Find the distance, in m, between the two poles A 8.19 B 9.74

C 11.00 D 12.19 S

P

10 m

20 m

Q

R 5m

S

19. In the diagram, PQ is a vertical pole. The angle of elevation of P from S is 450. Calculate the angle of depression of R from P A B

1402’ 36052’

P

R

Q

20. In the diagram, PS is a vertical pillar. The angle of depression of R from S is 200. Calculate the distance, in m, from Q to R

C 41025’ D 5308’

Angles of Elevation and Depression

4m

A B

132

5.40 7.42

C 7.64 D 9.40

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 42 0.

V S 3m

hm T

U

Calculate the value of h. A 10.4 B 12.0

C 14.1 D 17.9

SPM 2004 (July) 2. In Diagram , S, M and T are collinear points on a horizontal plane. SM = MT and TU is a vertical pole.

U 25 m

S

10 m

T M DIAGRAM 10

Angles of Elevation and Depression

133

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 

22 0 37  39 0 48

A C

0 B 50 12  0 D 67 23

SPM 2004 3. 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 B ∠PMQ

C ∠PMR D ∠PNR

4. In Diagram, PQ and RS are two vertical poles on a horizontal plane. R P Q

25 m 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 B 8.42

C 11.51 D 13.82

SPM 2005 (July)

Angles of Elevation and Depression

134

5. Diagram 17 shows two flats adjacent to each other on a horizontal plane. Four friends are seating at balconies P, Q, R and T respectively. Which of the following is the angle of elevation of P from R? A

 PRQ

B  PRT N

M

J

L

80 m

60 m K

DIAGRAM 8

C

 RPQ

D  RTP

6. In Diagram 8, J, K, L and M are four points on a horizontal ground. MN is a vertical pole 0 with the height of 20 m, JM = ML  JKL= 90

P JEBAT BLOCK

T Q

R

DIAGRAM 17

Angles of Elevation and Depression

135

TUAH BLOCK

Calculate the angle of elevation of vertex N from the point L A C

66 0 25  33 0 41

0 B 26 34  0 D 21 48

SPM 2005 7. Diagram below shows two vertical poles, PS and QR, on a horizontal plane. P Q 25 m S

10 m

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 B 41 0 59 '

C 57 0 59 ' D 68 0 11 '

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

Angles of Elevation and Depression

12 m

136

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 B 17.14

Angles of Elevation and Depression

C 18.13 D 20.92

137

angles

angles of elevation