HEIGHT AND DISTANCE

HEIGHT AND DISTANCE

1. The ratio of the length of a rod and its shadow °
is 1 : 3 . The angle of elevation of the sun.

3 (A) 18 m (B) 9 m

(A) 30° (B) 45° (C) 9.5 m (D) 6 m

(C) 60° (D) 90° 6. The length of a string between a kite and a
point on the ground is 90 m. The string makes
2. What is the angle of elevation of the Sun, when
an angle of 60° with the level the ground. If

x there is no slack in the string, then the height
the shadow of a pole of height x m is 3 m? of the kite is:

x°

x

3 (B) 45° (A) 90 3 m (B) 45 3 m
(A) 30°
(C) 180 m (D) 45 m
(C) 60° (D) 75°
7. An electric pole of 10 m high a steel wire is
3. The angle of the elevation of the sun at a fixed between top of pole and a point on earth
certain time is 60°. The height of the vertical by which pole kept straight. If steel wire make
pole that will cast a shadow of 30 m is: an angle of 45° from horizontal line which is

° passing through the line of the base of pole.

Find the length of steel.

(A) 30 3 m (B) 15 m

0 (D) 15 2 m °
(C) 3 m

4. Angle of depression of a car from 125 m high (A) 20 (B) 10 2
tower is 45°, then how much car is far from the
tower. (C) 10 (D) 5 2

° From the top of a light-house which is 20
8. metres above the sea-level, the angle of
depression of a ship is 30°. The distance of the
(A) 60 m (B) 75 m ship from the base of the light-house is

(C) 80 m (D) 125 m

5. A ladder lean against a wall makes an angle of °
60° with the ground. If the length of the ladder
is 19 m, find the distance of the foot of the
ladder from the wall.

1

(A) 20 m (B) 20 3 m 13. A vertical post 15 ft high is broken from a
certain height and its supper part which is, not

(C) 30 m (D) 30 3 m completely seperated, meet the ground and
make an angle of 30°. Find the height at which
9. From a point A on a bridge across a river, the
the post is broken.
angles of depression of the banks on opposite

sides of the river are 30° and 45°, respectively.

If the bridge is at a height of 9 m from the

surface of river, then find the width of the °

river.

A (A) 5 ft (B) 10 ft
°° (C) 7 ft (D) 4 ft

(A) 3 (B) 4 3 14. A straight tree breaks due to a storm and the

broken part bends so that the top of the tree

(C) 9( 3 +1) (D) 9 touches the ground making an angle of 30° with
the ground. The distance from the foot of the

10. Angle of elevation of top of temple which is tree to the point where the top touches the
situated on bank of a river from the both side ground is 10 metres. Find the height of the
of bank of river are 30° and 45° respectively. If tree?

height of the temple is 100 m. then find the

width of river. °

°°

(A) 100( 3 –1) (B) 10(1– 3 ) (A) 10( 3 +1) (B) 10 3
(C) 6 (D) 50 3 (C) 10( 3 –1) 10

(D) 3 m

11. A tree is broken by the wind. If the top of the 15. On walking 120m towards a chimney in a
tree struck the ground at an angle of 30° and horizontal line then the angle of elevation of
length of broken part is 30 m, then the height top of the chimney changes from 30° to 45°.
of the tree is The heightof the chimney is

° °°

(A) 25 3 m (B) 45 (A) 120 m (B) 60( 3 –1) m

(C) 15 3 m (D) 20 3 m (C) 60( 3 1) m (D) None of these

12. A pole has been broken by storm and the top of 16. Angle of elevation of a tower from a point on
the pole; touches the ground at a distance of
the ground is 30°. After waling 50 3 toward
20 m away from it with a angle of 30°. Find the
the tower the angle becomes 60° height of the
height of pole. tower is?

° °
3°

(A) 20 3 m (B) 60 3 m

(C) 40 3 m (D) 100 3 m (A) 75 m (B) 65 3 m
3 3 (C) 90 3 m (D) 60 3 m

2

17. The angle of elevationof the top of a tower from 21. The angle of elevation of the top of an

a certain point is 30°. If the observer moves 20 unfinished pillar at a point 150 m from its base

m towards the tower, the angle of elevation of is 30°. If the angle of elevation at the same

the top of the tower increases by 15°. The height point is to be 45°, then the pillar has to be

of the tower is. raised it’s height by how many metres?

°

°°

(A) 59.4 m (B) 61.4 m

(A) 17.3 m (B) 21.9 m (C) 62.4 m (D) 63.4 m

(C) 27.3 m (D) 30 m 22. An observer standing 72 m away from a

18. Angle of elevation of the top of a tower with building notices that the angles of elevation

any point on ground is 30°. When 100 m of the top and the bottom of a flagstaff on the

walking toward the tower then the angle of building are respectively 60° and 45°. The

elevation become 60°. Then find the height of height of the flagstaff is:

the tower.

°

°°
°

(A) 100 3 m (B) 25 3 m (A) 124.7 m (B) 52.7 m

(C) 101 3 m (D) 50 3 m (C) 98.3 m (D) 73.2 m

19. Angle of depression on the ground from the top 23. From the top of a cliff 90 m, high the anlges of
of the tower is 30°. When walking towards depression of the top and bottom of a tower
tower 40 m. then angle of depression becomes are observed to be 30° and 60° respectively.
45° then find the height of tower. The height of the tower is

°
°°

° (B) 40  3 1 m (A) 60 m (B) 75 m
(C) 30 m (D) 45 m
(A) 20  3 1 m

(C) 10 3 m (D) 20  3 1 m 24. The angles of elevation of an aeroplane flying
vertically above the ground as observed from

20. A man is watching a bike from the tower then two consecutive stones 1 km apart are 45° and
angle of depression is 45°. When car cover 200 60°. The height of the aeroplane above the
m. distance the toward the tower then angle of ground in km is:

depression becomes 60°. then find the height

of the tower?

°°

°

°

(A) 3 1 (B) 3 3
2 2

(A) 200 3 m (B) 200 3 m (C) 3+ 3 (D) 3 +1
3 1 3 1

(C) 300 3 m (D) 300 3 m 25. The tops of two poles of height 24 m and 36 m
3 1 3 1 are connected by a wire. If the wire makes an
angle of 60° with the horizontal, then the

3

length of the wire is

°°

°

(A) 8 3 m (B) 8 m  3  (B) 10

(A) 3

(C) 6 3 m (D) 6 m 20  3 1
3
26. An observer 1.6 m tall is 20 3 m away from a (C) 10 3 (D)

tower. The angle of elevation from his eye to 30. Angle of elevation of a zet plane from a point
the top of the tower is 30°. The height of the on earth is 60°, after 15 seconds flight angle

tower is: becomes 30°. If zet plane is flying 1500 3 m
above, at constant height then find the speed
3 of zet plane.
°

(A) 21.6 m (B) 23.2 m P°
°

(C) 24.72 m (D) None of these 3

27. A flagpost is surmounted on the wall. Angle of

elevation of top and bottom of flagpost made (A) 34.64 m/sec (B) 44.36 m/sec

by a man who is standing on other side of 40 m (C) 36.44 m/sec (D) 200 m/s

wife road are 60° and 45°. Find the height of

flagpost. 31. A man is watching from top of a tower a boat
speeding away from the tower. The boat makes
°° an angle of depression of 45° with the main’s
eys when at a distance of 60 metres from the
(A) 40 3 m (B) 20 3 m tower. After 5 seconds, the angle of depression
becomes 30°. What is the approximate speed
(C) 40( 3 –1) m (D) 20( 3 +1) m of the boat, assuming that it is running in still
water?

28. A man is standing away a distance of 50 m from °
a building. He make angle of 60° and 45° with °
the top and bottom of flag post which is
surmounted on top of building. Find the length
of flag post.

(A) 32 kmph (B) 36 kmph

° ° (C) 38 kmph (D) 40 kmph
50
(B) 3 32. An areoplane when flying at a height of 3125
m from the ground passes vertically below
(A) 50 3 m another plane at an instant when the angles
of elevation of the two planes from the same
(C) 50( 3 +1) (D) 50 ( 3 –1) point on the ground are 30° and 60°
respectively. The distance between the two
planes at that instant is:

29. From the top of a pillar of height 20 m, the °
angles of elevation and depression of the top °
and bottom of another pillar are 30° and 45°

respectively. The height of the second pillar

(in meters) is:

4

(A) 3125 m (B) 6000 m an angle q with the level ground such that tan

(C) 5000 m (D) 6250 m 15 
=  8 , how high is the kite, when there is no
33. A man on the top of a vertical tower observes a slack in the string?
car moving at a uniform speed coming directly
towards it. If it takes 12 minutes to change q
angle of depression 30° to 45°, how soon after
this, the car will reach the tower?

15 
tan  8 

°°

(A) 78.05 m (B) 75 m

(A) 14 minutes 23 sec (C) 316 m (D) 75.05

(B) 16 minutes 23 sec 37. At a point on the ground, the angle of elevation
(C) 15 minutes 23 sec of the top of a tower is found to be such that
(D) 17 minutes 23 sec
tan A = 8 . On walking 117 meters towards
15

34. An aeroplane flying at a height of 300 metres the tower, the angle of elevation is found to be

above the ground passes vertically above such that tan B = 3 . The height of the tower
another plane at an instant when the angle of 4
elevation of two planes from the same point
on the ground are 60° and 45°, respectively. is-

Find the height of the lower plane from the

ground, in metres, is 8
15
tan A =

tan B = 3
4
°°

(A) 100 3 (B) 50 (A) 212 m (B) 226 m
(C) 216 m (D) 232

100 (D) 150  3 1 38. At a point on level ground, the angle of
(C) 3 elevation of a vertical tower is found to be such

35. An aeroplane when at 1000 m height passes that its tangent is 5/12. On walking 192 metres

vertically above another at an instant when towards the tower the tangent of the angle of

the angles of elevation at the same observing elevation is 3/4. Find the height of the tower?

point are 45° and 30° respectively. How many

metres is lower one than the other? tan A = 5/12

tan B = 3/4

°° (A) 160 m (B) 180 m

(C) 240 m (D) 260 m

(A) 442.6 m (B) 422.6 m 39. At a point on a horizontal line though the base
(C) 482.6 m (D) 444.6 m of a monument the angle monument is found

36. The length of a string between a kite and a to be such that its tangent is 1 . On walking
point on the ground is 85 m. If the string makes 5

5

138 metres towards the monument the secant (A) 50 m (B) 48 m

of the angle of elevation is found to be 193 . (C) 25 m (D) 24 m
12
43. A building is 10 3 m high and two point P and Q
The height of the monument (in metre) is: seeing from top of the building. If angle of
depression of these point mutually
tan A = 1 complementary and PQ = 20 m then. Find the
5 distance of end point from building.

193 3 P
12 Q
sec B = PQ = 20

(A) 35 (B) 49 (A) 30 m (B) 40 m

(C) 42 (D) 56 (C) 25 m (D) 45 m

40. The length of a string of a kite from a point on 44. A vertical stick 12 m long cast a shadow of 8 m
the ground is 65 m. If the string makes an angle long on the ground. At the same time, a tower

a° with the level ground such that a= 12 , how cast a shadow of 40 m long on the ground. The
5 height of the tower is.

high is the kite?

a° a= 12
5
(A) 60 m (B) 65 m

(a) 60 m (b) 40 m (C) 70 m (D) 72 m

(c) 35 m (d) 25 m 45. The angle of elevation of a cloud from a point

41. Angle of elevation of top of a tower from two 200 m above a lake is 30° and the angle of
points which are situated at a distance of ‘a’ depression of its reflection in the lake is 60°.
and ‘b’ from the base of tower are The height of the cloud is

complemetary to each other. Find the height

of tower. ° °

ab

(A) 200 m (B) 300 m

(A) a  (B) a  (C) 400 m (D) 600 m

a 46. The angle of elevation of a cloud from a point
b
(C) ab (D) h metres above the surface of a lake is 30° and
the angle of depression of its reflection is 60°.

42. The angles of elevation of the top of a tower Then the height the cloud above the surface of
from two points situated at distances of 36 m the lake is

and 64 m from its bease and in the same h°
straight line are complementary to each other. °
What is the height of the tower?

(A) h 3 metres (B) h metres
(C) h 2 metres (D) 2 h metres

6

47. A spherical beallon of radius r subtends angle PREVIOUS YEARS
of 60° at the eye of an observer. If the angle of

elevation of its centre is 60° and h is the height QUESTIONS
of the centre of the balloon, then which one of

the following is correct? 51. Two points P and Q are at the distance of x and

r y (where y > x) respectively from the base of a

° ° building and on a straight line. If the angles of
elevation of the top of the building from points
h P and Q are complementary, then what is the

(A) h = r (B) h = 2r height of the building?

(C) h = 3r (D) h = 2r PQ x
y y>x

48. Radius of spherical ballon which is flying on PQ
air is 10 ft. if angle of elevationof centre of
ballon from a point on the ground is 45° and CGL Mains 2018
the ballon subtends an angle of 60° cm on at
that point. Then find the height of centre of (A) xy (B) y
from the plane. x

(C) x (D)  xy
y

(A) 10 ft (B) 15 ft 52. The tops of two poles of height 60 metres and
35 metres and connected by a rope. If the rope
makes an angle with the horizontal whose tan-

(C) 20 2 ft (D) 10 2 ft gent is 5 metres, then what is the distance (in
9
49. Angle of top of a building from top and bottom
of a tree are x and y respectively if height of metres) between the two poles?
tree is h m then height of building is
60 35

xy h 5
9

h cot x h cot y (A) 63 CGL Mains 2018
(A) cot x  cot y (B) cot x  cot y (B) 60

h cot x h cot y (C) 25 (D) 45

(C) cot x  cot y (D) cot x  cot y 53. A Navy captain going away from a lighthouse

50. Angle of elevation of top of a building and at the speed of 4[( 3 ) – 1] m/s. He observes that

chimney from a point on the ground are x and it takes him 1 minute to change the angle of

45° respectively then find the height of elevation of the top of the lighthouse from 60º

chimney (in m.)? to 45º. What is the height (in metres) of the

lighthouse?

x° 4[( 3 ) – 1]

(A) hcotx + h (B) hcotx – h 60º 45º
(C) htan – h (D) htanx – h

7

CGL Mains 2018

(A) 240 3 (B) 480[( 3 ) – 1] 4

(C) 360 3 (D) 280 2 3

54. Two trees are standing along the opposite sides CGL Mains 2018

of a road. Distance between the two trees is 400 (A) 720 (B) 960

metres. There is a point on the road between (C) 840 (D) 1030
the trees. The angle of depressions of the point

from the top of the trees are 45º and 60º. If the 57. On walking 100 metres towards a building in a

height of the tree which makes 45º angle is 200 horiozontal line, the angle of elevation of its

metres, then what will be the height (in metres) top changes from 45º to 60º. What will be the

of the other tree? height (in metres) of the building?

400 100
45º 60º

45º 60º 45º CGL Mains 2018
200

(A) 50 (3 + 3 ) (B) 100 ( 3 + 1)

CGL Mains 2018 (C) 150 (D) 100 3

(A) 200 (B) 200 3 58. The upper part of a tree broken over by the wind
(C) 100 3 (D) 250 make an angle of 60º with the ground. The dis-
tance between the root and the point where top
55. A tower stands on the top of a building which is of the tree touches the ground is 25 metres.
40 metres high. The angle of depression of a What was the height (in metres) of the tree?
point situated on the ground from the top and
bottom of the tower are found to be 60º and 45º 60º
respectively. What is the height (in metres) of 25
tower?

40

60º (A) 84.14 CGL Mains 2018
(B) 93.3
45º
(A) 20 3 CGL Mains 2018 (C) 98.25 (D) 120.24

(B) 30( 3 + 1) 59. The height of a tower is 300 meters. When its
top is seen from top of another tower, then the
(C) 40( 3 – 1) (D) 50( 3 – 1) angle of depression is 60º. The horizontal dis-
tance between the bases of the two towers is
56 From a point, P the angle of elevation of a tower 120 metres. What is the height (in metres) of
the small tower?
3
is such that its tangent is 4 . On walking 560 300
metres towards the tower the tangent of the

4 60º
angle of elevation of the tower becomes 3 . 120
What is the height (in metres) of the tower?

P CGL Mains 2018
(B) 106.71
3 (A) 88.24 (D) 112.64
4 560 (C) 92.15

8

60. The angle of elevation of an aeroplane from a 38 58
point on the ground is 60º. After flying for 30 52
seconds, the angle of elevation changes to 30º.
If the aeroplane is flying at a height of 4500 m, CGL Mains 2018
then what is the speed (in m/s) of aeroplane?

(A) 46 (B) 42

60º 30 (C) 44 (D) 48
30º
4500 The angles of elevation of the top of a tree 220
64. meters high from two points lie on the same
plane are 30º and 45º. What is the distance (in
CGL Mains 2018 metres) between the two points?

(A) 50 3 (B) 100 3 220

30º 45º

(C) 200 3 (D) 300 3

61. A kite is flying in the sky. The length of string CGL Mains 2018

between a point on the ground and kite is 420 (A) 193.22 (B) 144.04

m. The angle of elevation of string with the

ground is 30º. Assuming that there is no slack (C) 176.12 (D) 161.05

in the string, then what is the height (in metres) 65. The angles of elevation of the top of a tower 72
of the kite? metre high from the top and bottom of a build-
ing are 30º and 60º respectively. What is the
420 height (in metres) of building?
30º
72
30º 60º

CGL Mains 2018

(A) 210 (B) 140 3 CGL Mains 2018

(C) 210 3 (D) 150 (A) 40 (B) 20 3

62. A balloon leaves from a point P rises at a (C) 24 3 (D) 48
unifrom speed. After 6 minutes, an observer
situated at a distance of 450 3 metres from 66. From the top of a tower, the angles of depres-
sion of two objects on the ground on the same
point P observes that angle of elevation of the side of it, are observed to be 60º and 30º re-
balloon is 60º. Assume that point of observa- spectively and the distance between the objects
tion and point P are on the same level. What is
the speed (in m/s) of the balloon? is 400 3 m. The height (in m) of the tower is:

P (side) 60º 30º
400 3
6 P 450 3
60º

P

CGL Mains 2019

CGL Mains 2018 (A) 800 (B) 800 3

(A) 4.25 (B) 3.75 (C) 600 3 (D) 600

(C) 4.5 (D) 3.45

63. The distance between the tops of two building 67. From a point exactly midway between the foot
38 metres and 58 metres high iss 52 metres. of two towers P and Q, the angles of elevation
of their tops are 30º and 60º, respectively. The
What will be the distance (in metres) between ratio of the height of P to that of Q is:

two buildings?

9

P Q top of the pole as observed from P and Q are 60º
Q and 30º, respectively and the distance between
30º 60º P
them is 84 3 m. What is the height (in m) of
CGL Mains 2019 the pole?

(A) 1 : 3 PQ P Q,
(B) 1 : 2 60º 30º 84 3

(C) 1 : 2 3

(D) 2 : 3 3 (A) 60 CGL Mains 2019
(C) 73.5 (B) 63
68. P and Q are two points on the ground on either (D) 52.5
side of a pole. The angles of elevation of the

ANSWER KEY

1. (A) 11. (A) 21. (D) 31. (A) 41. (C) 51. (C) 61. (A)
2. (C) 12. (D) 22. (B) 32. (D) 42. (B) 52. (D) 62. (B)
3. (A) 13. (D) 23. (A) 33. (B) 43. (A) 53. (A) 63. (D)
4. (D) 14. (C) 24. (B) 34. (A) 44. (A) 54. (B) 64. (D)
5. (C) 15. (C) 25. (B) 35. (B) 45. (C) 55. (C) 65. (D)
6. (B) 16. (A) 26. (A) 36. (B) 46. (D) 56. (B) 66. (D)
7. (B) 17. (C) 27. (A) 37. (C) 47. (C) 57. (A) 67. (A)
8. (B) 18. (D) 28. (A) 38. (B) 48. (D) 58. (B) 68. (B)
9. (B) 19. (A) 29. (A) 39. (C) 49. (C) 59. (C)
10. (A) 20. (A) 30. (D) 40. (A) 50. (B) 60. (B)

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