1)

An observer on the top of a tree finds the angle of depression of a car moving towards the tree to be 30 degrees. After 3 minutes, this angle becomes 60 degrees. After how much more time will the car reach the tree?

A)

1.5 min

B)

2 min

C)

4 min

D)

4.5 min

2)

A house of height 100 metres subtends a right angle at the window of an opposite house. If the height of the window is 64 metres, then the distance between the two houses is

A)

36 m

B)

48 m

C)

60 m

D)

54 m

3)

The height of a house subtends a right angle at an opposite window & the line through the window to the top of the house makes an angle θ with the vertical. If the breath of the street be ‘d’ meters. Find the height of the house

A)

d.sinθ.cosθ

B)

d.sinθ.secθ

C)

d.secθ.cosecθ 

D)

d.cosθ.cosecθ

4)

From the top and bottom of a straight hill, the angle of depression and elevation of the top of a pillar of 10 m height are observed to be 60° and 30° respectively. The height (in metres) of the hill is

A)

30

B)

40

C)

60

D)

80

5)

The distance between two parallel poles is 40√3 m. The angle of depression of the top of the second pole when seen from the top of first pole is 30°. What will be the height of second tower if the first pole is 100m long?

A)

50√3 m

B)

80 m

C)

35√3 m

D)

60 m

6)

From the top of a tower of height 180 m the angles of depression of two objects on either sides of the tower are 30° and 45°. Then the distance between the objects are

A)

180 (3 + √3) m

B)

180 (3 - √3) m

C)

180 (√3 - 1) m

D)

180 (√3 + 1) m

7)

A vertical pole and a vertical tower are standing on the same level ground. Height of the pole is 10 metres. From the top of the pole the angle of elevation of the top of the tower and angle of depres­sion of the foot of the tower are 60° and 30° respectively. The height of the tower is

A)

20 m

B)

30 m

C)

40 m

D)

50 m

8)

The angle of elevation of the top of a vertical tower situated perpendicularly on a plane is observed as 60° from a point P on the same plane. From another point Q, 10 m vertically above the point P, the angle of depression of the foot of the tower is 30°. The height of the tower is

A)

15 m

B)

20 m

C)

25 m

D)

30 m

9)

There are two temples, one on each bank of a river just opposite to each other. One temple is 54 m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are 30° and 60° respectively. The height of the temple is

, Avg: 01:18 , 100%✓

A)

18 m

B)

36 m

C)

18√3 m

D)

36√3 m

10)

There are two verticals posts, one on each side of a road, just opposite to each other.One post is 108 metre high. From the top of this post, the angles of depression of the top and foot of the other post are 30° and 60° respectively. The height of the other post, in metre is:

A)

36

B)

72

C)

108

D)

110

11)

From an aeroplane just over a river, trees on the opposite bank of the river are found to be 60° and 30° respectively. If the breadth of the river is 400 m, then the height of the airplane above the river at  an instant is 
(assume √3 = 1.732)

A)

173.2 m

B)

346.4 m

C)

519.6 m

D)

692.8 m

12)

The tops of two poles of height 24 m and 36 m are connected by wire. If the wire makes an angle of 60° with the horizontal, then the length of the wire is. 

A)

8√3 m

B)

6√3 m

C)

8 m

D)

6 m

13)

A pole stands vertically inside a scalene triangular park ABC. If the angle of elevation of the top of the pole from each corner of the park is same, then in ΔABC, the foot of the pole is at the

, Avg: 01:02 , 100%✓

A)

centroid

B)

circumcentre

C)

incentre

D)

orthocentre

14)

Two posts are x metres apart and the height of one is double that of the other. If from the mid-point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then the height (in meters) of the shorter post is

, Avg: 01:20 , 29%✓

A)

\({x\sqrt{2}}\)

B)

\({x\over \sqrt{2}}\)

C)

\({x\over 2\sqrt{2}}\)

D)

\({x\over 4}\)

15)

Two poles of equal height are standing opposite to each other on either side of a road which is 100 m wide. From a point between them on road, angles of elevation of their tops are 30° and 60°. The height of each pole in meter, is:

A)

20√3 m

B)

25√3  m

C)

28√3  m

D)

30√3 m

16)

The angles of elevation of the top of a building from the top and bottom of a tree are x and y respectively. If the height of the tree is h meter then, in meter, the height of the building is:

A)

\({h.cotx \over cotx + coty}\)

B)

\({h.cotx \over cotx - coty}\)

C)

\({h.coty \over cotx + coty}\)

D)

\({h.coty \over cotx - coty}\)

17)

The distance between two pillars of length 16 m and 9 m is x meters. If two angles of elevation of their respective top from the bottom of the other are complementary to each other, then the value of x in meters is

A)

9

B)

12

C)

15

D)

16

18)

If a pole of 12 m height caste a shadow of 4√3 m long on the ground then the sun's angle of el­evation at that instant is

A)

30°

B)

45°

C)

60°

D)

90°

19)

A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40 m long on the ground. The height of the tower

A)

60 m

B)

65 m

C)

70 m

D)

72 m

20)

The shadow of the tower becomes 60 meters longer when the altitude of the sun changes from 45° to 30°. Then the height of the tower is

A)

20(√3 + 1) m

B)

24(√3 + 1) m

C)

30(√3 + 1) m

D)

30(√3 - 1) m

21)

If the angle of elevation of the Sun changes from 30° to 45°, the length of the shadow of a pillar decreases by 20 meters . The height of the pillar is:

A)

20 (√3 - 1)m

B)

20 (√3 + 1)m

C)

10 (√3 - 1)m

D)

10 (√3 + 1)m

22)

A ladder is placed along a wall such that its upper end is touching the top of the wall. The foot of the ladder is 10 ft away from the wall and the ladder is making an angle of 60° with the ground. When a man starts dimning on it, it slips and now ladder makes an angle of 30° with ground. How much did the ladder slip vertically?

A)

10(√3 - 1 ) ft.

B)

10(3 - √3) ft.

C)

20(3 - √3) ft.

D)

20(√3 - 1 ) ft.

23)

A vertical post 15 ft. high is broken at a certain height and its upper part, not completely separated meets the ground at an angle of 30°. Find the height at which the post is broken

A)

10 ft.

B)

5 ft.

C)

15 ft.

D)

20 ft.

24)

The angle of elevation of an aeroplane from point A on the ground is 60°. After flight of 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of 1500√3 m, find the speed of the plane in km/hr.

A)

720 km/hr

B)

900 km/hr

C)

1000 km/hr

D)

1200 km/hr

25)

An aeroplane when flying at a height of 5000 m from the ground passes vertically above another aeroplane at an instant, when the angles of elevation of the two aeroplanes from the same point on the ground are 60° and 45° respectively, the vertical distance between the aeroplanes at that instant is:

A)

5000 (√3 - 1) m

B)

5000 (3 - √3) m

C)

5000 (\(1-{1 \over {\sqrt{3}}}\)) m

D)

4500 m

26)

From a point P on the ground, the angle of elevation of the top of a 10m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff (Take √3 = 1.732)

A)

17.32m

B)

7.32m

C)

1.32m

D)

5.32m

27)

The angle of elevation of the top of a chimney and roof of the building from a point on the ground are x and 45° respectively. The height of buidling is h metre. Then the height of the chimney,(in metre) is

A)

h cot x + h

B)

h cot x - h

C)

h tan x - h

D)

h tan x + h

28)

From two points on the ground lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distance of the two points from the foot of the pillar are 9 metres and 16 metres and the two points lie on the same side of the pillar . Then the height of the pillar is

A)

5m

B)

10m

C)

9m

D)

12m

29)

A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30°. The man walks some distance to­wards the tower and then his angle of elevation of the top of the tower is 60°. If the height of tower is 30m, then the distance he moves is

A)

22m

B)

22√3m

C)

20m

D)

20√3m

30)

At a point on a horizontal line through the base of a monument, the angle of elevation of the top of the monument is found to be such that its tangent is 1/5 . On walking 138 meters towards the monument the secant of the angle of elevation is found to be √193/12. The height of the monument (in metre) is

A)

42

B)

49

C)

35

D)

56

31)

A tower standing on a horizontal plane subtends a certain angle at a point 160 m apart from the foot of the tower. On advancing 100 m to­wards it, the tower is found to sub­tend an angle twice as before. The height of the tower is

A)

80m

B)

200m

C)

100m

D)

160m

32)

The angle of elevation of the top of a tower from the point P and Q at a distance of 'a' and 'b' respectively from the base of the tower and in the same straight line with it are complementary. The height of the tower is:

A)

√ab

B)

a/b

C)

ab

D)

a²b²

33)

The angle of elevation of the top of a tower from a point A on the ground is 30°. On moving a dis­tance of 20 metres towards the foot of the tower to a point B, the angle of elevation increases to 60°. The height of the tower is

, Avg: 01:03 , 87%✓

A)

√3m

B)

5√3m

C)

10√3m

D)

20√3m

34)

A person observes that the angle of elevation at the top of a pole of height 5 meters is 30°. Then the distance of the person from the pole is:

A)

5√3

B)

5/√3

C)

√3

D)

10√3

35)

A coconut tree swings with the wind in such a manner that the angle covered by its trunk is 18 degrees. If the topmost portion of the tree covers a distance of 44 metres,find the length of the tree.

SSC CGL 2022

A)

140 metres

B)

210 metres

C)

120 metres

D)

70 metres

36)

A ladder 18 m long rests against a wall so that the angle between the ladder and the wall is 30°. How far (in m) is the base of the ladder from the wall?

, Avg: 00:33 , 66%✓ SSC CGL 2022

A)

\(18 \sqrt{3}\)

B)

9

C)

\(9 \sqrt{3}\)

D)

18

37)

The length of the shadow of a vertical tower on level ground increases by 8.4 m when the altitude of the sun changes from 45° to 30°. What is the height of the tower (in m)?

, Avg: 01:41 , 50%✓ SSC CGL 2022

A)

\(4.2( \sqrt 3 + 1)\)

B)

\(8.4( \sqrt 3 + 3)\)

C)

\(4.2( \sqrt 3 + 3)\)

D)

\(4.2( \sqrt 3 - 1)\)

38)

From a ship's masthead 180 m high, the angle of depression of a boat is observed to be 60°. Find the distance (in m) of the boat from the ship.

, Avg: 01:00 , 71%✓ SSC CGL 2022

A)

360

B)

\(60 \sqrt{3}\)

C)

\(180 \sqrt{3}\)

D)

180

39)

A ladder of length 3.5 m just reaches the top of a wall. If the ladder makes an angle of 60° with the wall, then what is the height of the wall (in m)?

, Avg: 00:54 , 28%✓ SSC CGL 2022

A)

\(\frac{3.5}{\sqrt{3}}\)

B)

\(\frac{7 \sqrt{3}}{4}\)

C)

\(3.5 \sqrt{3}\)

D)

1.75

40)

A and B are two points on the same side of a ground, 50 meters apart. The angles of elevation of these points to the top of a tree are 60° and 30, respectively. What is 40% of the height of the tree (in m)?

SSC CGL 2022

A)

\(10 \sqrt3\)

B)

\(15 \sqrt3\)

C)

\(25\sqrt{3}\)

D)

\(5 \sqrt3\)

41)

The tops of two poles of heights 18 m and 30.5 m are connected by a wire. If the wire makes an angle of 30° with the horizontal, what is the length (in m) of the wire?

, Avg: 00:50 , 100%✓ SSC CGL 2022

A)

36

B)

28

C)

20

D)

25

42)

What is the angle of elevation of the sun when the shadow of a 9-m high pole is \(3\sqrt 3\) m long?

, Avg: 00:32 , 53%✓ SSC CGL 2022

A)

60°

B)

90°

C)

45°

D)

30°

43)

A 20 m long ladder rests against a wall so that the angle between the ladder and the wall is 30°. How far (in m) is the base of the ladder from the wall?

, Avg: 01:06 , 33%✓ SSC CGL 2022

A)

20

B)

20√3

C)

10√3

D)

10

44)

The length of the shadow on the ground of a tall tree of height 30 m is 10√3 m. What is the angle (in degrees) of elevation of the sun?

, Avg: 00:45 , 77%✓ SSC CGL 2022

A)

60

B)

30

C)

45

D)

15

45)

From the top of a 195-m high cliff, the angles of depression of the top and bottom of a tower are 30^∘ and 60^∘, respectively. Find the height of the tower (in m).

, Avg: 01:04 , 28%✓ SSC CGL 2022

A)

130

B)

195

C)

195√3

D)

65

46)

A poster is on top of a builiding. A person is standing on the ground at a distance of 50 m from the building. The angles of elevation to the top of the poster and bottom of the poster are 45° and 30, respectively. What is 200% of the height (in m) of the poster?

, Avg: 01:40 , 45%✓ SSC CGL 2022

A)

\({25\over3}(3 - \sqrt {3})\)

B)

\({75\over3}(3 - \sqrt {3})\)

C)

\({50\over3}(3 - \sqrt {3})\)

D)

\({100\over3}(3 - \sqrt {3})\)

47)

Two poles of heights 10 m and 17 m are fixed to a level ground. The distance between the bottom of the poles is 24 m. What is the distance (in m) between their tops?

, Avg: 01:06 , 100%✓ SSC CGL 2022

A)

30

B)

25

C)

24

D)

27

48)

Exactly midway between the foot of two towers P and Q, the angles of elevation of their tops are 45° and 60°, respectively. The ratio of the heights of P and Q is:

, Avg: 00:41 , 50%✓ SSC CGL 2022

A)

1 : 3

B)

√3 : 1

C)

1 : √3

D)

3 : 1

49)

The length of the shadow on the ground of a tall tree of height 45 m is 15√3 m. What is the angle (in degrees) of elevation of the sun?

, Avg: 00:36 , 60%✓ SSC CGL 2022

A)

60°

B)

45°

C)

30°

D)

90°

50)

From a point P on a level ground, the angle of elevation of the top of the tower is 30°. If the distance of point P from the foot of the tower is 510 m, then 50% of the height of the tower (in m) is:

, Avg: 00:34 , 90%✓ SSC CGL 2022

A)

\(150\sqrt{3}\)

B)

\(85\sqrt{3}\)

C)

85

D)

\(\frac{85\sqrt{3} }{3}\)

51)

A kite flying at a height of 120 m is attached to a string which makes an angle of 60° with the horizontal. What is the length (in m) of the string?

SSC CGL 2022

A)

\(80\sqrt 3\)

B)

\(90\sqrt 3\)

C)

\(75\sqrt 3\)

D)

\(84\sqrt 3\)

52)

From a point P on a level ground, the angle of elevation of the top of a tower is 30°. If the tower is 110√3 m high, what is the distance (in m) of point P from the foot of the tower?

, Avg: 00:33 , 78%✓ SSC CGL 2022

A)

115

B)

220

C)

330

D)

110

53)

The angle of elevation of the top of a tall building from the points M and N at the distances of 72 m and 128 m, respectilvely, from the base of the building and in the same straight line with it, are complementary. The height of the building (in m) is:

, Avg: 02:00 , 62%✓ SSC CGL 2022

A)

80

B)

96

C)

84

D)

90

54)

A vertical pole and a vertical tower are on the same level ground in such a way that, from the top of the pole, the angle of elevation of the top of the tower is 60° and the angle of depression of the bottom of the tower is 30°. If the height of the pole is 24 m, then find the height of the tower (in m).

, Avg: 01:03 , 42%✓ SSC CGL 2022

A)

72

B)

\(24(\sqrt3+1)\)

C)

\(24\sqrt3(\sqrt3+1)\)

D)

96

55)

A kite is attached to a string. Find the length of the string (in m) when the height of the kite is 90 m and the string makes an angle of 30° with the ground.

, Avg: 00:35 , 75%✓ SSC CGL 2022

A)

45

B)

\({60 \sqrt{3} }\)

C)

180

D)

\({90\sqrt{3} }\)

56)

A vertical pole and a vertical tower are on the same level of ground in such a way that from the top of the pole, the angle of elevation of the top of the tower is 60º and the angle of depression of the bottom of the tower is 30º. If the height of the tower is 76 m, then find the height (in m) of the pole.

, Avg: 01:30 , 57%✓ SSC CGL 2022

A)

38

B)

57

C)

19√3

D)

19

57)

A pole 23 m long reaches a window which is 3√5 m above the ground on one side of a street. Keeping its foot at the same point, the pole is turned to the other side of the street to reach a window 4√15m high. What is the width (in m) of the street?

, Avg: 02:03 , 71%✓ SSC CGL 2022

A)

22

B)

17

C)

39

D)

35

58)

The angle of elevation of the top of an unfinished tower at a point distant 78 m from its base is 30°. How much higher must the tower be raised (in m) so that the angle of elevation of the top of the finished tower at the same point will be 60º?

, Avg: 01:10 , 57%✓ SSC CGL 2022

A)

52√3

B)

26√3

C)

80

D)

78√3

59)

Let A and B be two towers with the same base. From the mid point of the line joining their feet, the angles of elevation of the tops of A and B are 30° and 45°, respectively. The ration of the heights of A and B is:

, Avg: 00:42 , 100%✓ SSC CPO 2020

A)

√3 : 1

B)

1 : 3

C)

1 : √3

D)

3 : 1

60)

A ladder is resting against a wall, The angle between the foot of the ladder and the wall is 45° and the foot of the ladder is 6.6 m away from the wall. The length of the ladder (in m) is:

, Avg: 01:14 , 100%✓ SSC CPO 2020

A)

6.6 X √2

B)

3.3 X √2

C)

2.2 X √2

D)

3.6 X √2

61)

A Person was standing on a road near a mall. He was 1215 m away from the mall and able to see the top of the mall from the road in such a way that the top of a tree, which is in between him and the mall, was exactly in line of sight with the top of the mall. The tree height is 20 m and it is 60 m away from him. How tall (in m) is the mall ?

SSC CPO 2020

A)

405

B)

375

C)

300

D)

250

62)

A ladder leaning against a wall makes an angle θ with the horizontal ground such that tan θ = 12/5. If the height of the top of the ladder from the wall is 24 m., then what is the distance (in m) of the foot of the ladder from the walI ?

SSC CPO 2020

A)

19.5

B)

10

C)

18

D)

7.5

63)

Let A and B be two towers with same base. From the midpoint of the line joining their feet, the angles of elevation of the tops of A and B are 30° and 60°, respectively. The ratio of the heights of B and A is:

SSC CPO 2020

A)

3 : 1

B)

1: √ 3

C)

1 : 2

D)

1 : 3

64)

A ladder is resting against a wall. The angle between the foot of the ladder and wall is 60°, and the foot of the ladder is 3.6 m away from the wall. The length of the ladder (in m) is:

, Avg: 00:56 , 100%✓ SSC CPO 2020

A)

5.4

B)

14.4

C)

3.6

D)

7.2

65)

Asha and Suman's mud forts have heights 9 cm and 16 cm. If the fort tops are at 25 cm apart from each other, then the distance (in cm) between two forts is:

, Avg: 01:11 , 100%✓ SSC CPO 2020

A)

7

B)

16

C)

25

D)

24

66)

The length of the shadow of a vertical pole on the ground in 36 m. If the angle of elevation of the sun at that time is θ, such that secθ = (13/12) then what is the height (in cm) of the pole?

, Avg: 00:24 , 100%✓ SSC CPO 2020

A)

12

B)

15

C)

18

D)

9

67)

Asha and Suman's mud forts have heights 9 cm and 16 cm. They are 24 cm apart. How far (in cm) are the fort tops from each other?

SSC CPO 2020

A)

25

B)

16

C)

24

D)

7

68)

The length of the shadow of a vertical pole on the ground is 18 m. If the angle of elevation of the sun at that time is θ, such that \(\cos \theta = \frac {12}{13} \), then what is the height (in m) of the pole?

SSC CPO 2020

A)

7.5

B)

9

C)

18

D)

12

69)

A ladder leaning against a wall makes an angle θ with the horizontal ground such that \( \cos \theta = \dfrac{5}{13} \). If the height of the top of the ladder from the foot of the wall is 18 m, then what is the distance (in m) of the foot of the ladder from the wall?

, Avg: 00:59 , 42%✓ SSC CPO 2020

A)

19.5

B)

7.5

C)

13

D)

18

70)

A person was standing on a road near a mall. He was 1425 m away from the mall and able to see the top of the mall from the road in such a way that the top of a tree, which is in between him and the mall, was exactly in line of sight with the top of the mall. The height of the tree is 10 m and it is 30 m away from him. How tall (in m) is the mall?

, Avg: 01:21 , 100%✓ SSC CPO 2020

A)

475

B)

300

C)

525

D)

425

71)

At a particular time, the length of the shadows of a pole and that of a tower are, respectively, 12 m and 27 m. If the height of the pole is 24 m, what is the height (in m) of the tower?

SSC Selection Post Matric 2022

A)

54

B)

63

C)

45

D)

36

72)

A ladder 10 m long rests against a vertical wall making an angle of 30° with the wall. How high up (in m) does it reach the wall from the ground? (Take \(\sqrt 3 = 1.73.\))

, Avg: 00:33 , 50%✓ SSC CHSL 2021

A)

8.56

B)

8.65

C)

5.88

D)

5

73)

The angle of elevation of a ladder against a wall is 45°. The length of the ladder is 12 m. What is the distance between the wall and the foot of the ladder?

, Avg: 00:55 , 100%✓ SSC CHSL 2021

A)

\(6\sqrt 2 \ m\)

B)

\(3\sqrt 2 \ m\)

C)

\(5\sqrt 3 \ m\)

D)

\(4\sqrt 3 \ m\)

74)

As observed from the top of a lighthouse, 42 m high above sea-level, the angle of depression of a ship sailing directly towards it changes from 30° to 45°. The distance travelled by the ship during the period of observation is:

, Avg: 00:54 , 50%✓ SSC CHSL 2021

A)

\(42(\sqrt 3 - 1)\)

B)

\(42(\sqrt 3 + 1)\)

C)

42

D)

\(42(1 - \sqrt 3 )\)

75)

The string of a kite is 158 m long and it makes an angle of 30° with the horizontal. What is the height (in m) of the kite ?
Assume there is no slack in the string.

, Avg: 00:55 , 100%✓ SSC CHSL 2021

A)

99

B)

79

C)

100

D)

80

76)

A kite is flying at a height of 138 m above the ground. It is attached to a string inclined at 45° to the horizontal. What is the approximate length (in m) of the string?

SSC CHSL 2021

A)

193

B)

194

C)

190

D)

195

77)

A straight vertical pole was broken during a cyclone in such a way that its top touched the ground at a distance of  \(6\sqrt 3\)  m from the bottom of the pole and made and angle of 30° with the horizontal. What was the height (in m) of the pole?

, Avg: 00:45 , 43%✓ SSC CHSL 2021

A)

12

B)

18

C)

\(12\sqrt 3\)

D)

\(18\sqrt 3\)

Correct Option: B

18

---

In fig, we have to calculate P + H

tan 30° = P/6√3, P = 6m

Also, sin 30° = P/H, we get H= 12m

thus, P + H = 18m

 

78)

The angle of elevation of the top of a pillar from the foot and the top of a building 20 m high, are 60° and 30° respectively. The height of the pillar is

SSC CGL 2016

A)

3 m

B)

9 m

C)

27 m

D)

30 m

79)

From a point exactly midway between the foot of two towers P and Q,the angles of elevation of their tops are \(30^0\)and \(60^0\), respectively. The ratio of the height of P to that of Q is:

, Avg: 00:56 , 66%✓ SSC CGL 2019

A)

1 : 3

B)

1 : 2

C)

\(1:2\sqrt3\)

D)

\(2 : 3\sqrt3\)

Correct Option: A

1 : 3

---

\(tan 30 = {1\over \sqrt{3}} = {P\over x}\)   ;

  \(tan 60 = { \sqrt{3}} = {Q\over x}\)

\({P\over Q} = {1\over 3}\)

80)

P and Q are two points on the ground on either side of a pole. The angles of elevation of the top of the pole as observed from P and Q are \(60^0\) and \(30^0\), respectively and the distance between them is \(84\sqrt3\)m. What is the height (in m) of the pole?

, Avg: 02:25 , 50%✓ SSC CGL 2019

A)

63

B)

73.5

C)

52.5

D)

60

81)

From the top of a tower, the angles of depression of two objects on the ground on the same side of it, are observed to be \( 60^\circ and 30^\circ\) respectively and the distance between the objects is \(400 \sqrt3\) metre. The height (in metre) of the tower is:

, Avg: 01:10 , 75%✓ SSC CGL 2019

A)

800

B)

\(800\sqrt3\)

C)

600

D)

\(600\sqrt3\)

Correct Option: C

600

---

BC = \(400 \sqrt3 \)m;
In \(\triangle ACD\),
tan \(60^0 = \frac{\sqrt{3}}{1} = \frac{AD}{CD}\);
In\( \triangle ABD\),
tan \(30^0 = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3} = \frac{AD}{BD};\)
BC = BD - CD = 3 - 1 = 2 units;
2 units = 400 x
\(\sqrt{3} \)units =\( \frac{400 \sqrt3}{2} \times \sqrt{3}\) = 600 m

82)

\(\)Seema flies a kite on a 16 m string at an inclination of 60 degree. What is the height of the kite above the ground?

, Avg: 00:44 , 84%✓ SSC CGL 2020

A)

\({4 \sqrt3} m\)

B)

\({16 \sqrt3} m\)

C)

\({6 \sqrt3} m\)

D)

\({8 \sqrt3} m\)

Correct Option: D

\({8 \sqrt3} m\)

---

\(sin60^o = {\sqrt3 \over2}={AB \over AC}\),

\(AB = 8\sqrt3 m\)