216188height & Distance All Sheets - Crwill
216188height & Distance All Sheets - Crwill
216188height & Distance All Sheets - Crwill
3
(A) 18 m (B) 9 m
(C) 9.5 m (D) 6 m
(A) 30° (B) 45°
6. The length of a string between a kite and a
(C) 60° (D) 90°
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 m? of the kite is:
3
x
°
x
3
(A) 90 3 m (B) 45 3 m
(A) 30° (B) 45°
(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 °
(C) m (D) 15 2 m
3
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
°
8. From the top of a light-house which is 20
metres above the sea-level, the angle of
(A) 60 m (B) 75 m depression of a ship is 30°. The distance of the
(C) 80 m (D) 125 m ship from the base of the light-house is
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 Maths By Adutiya Sir
(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
14. A straight tree breaks due to a storm and the
(A) 3 (B) 4 3 broken part bends so that the top of the tree
touches the ground making an angle of 30° with
(C) 9( 3 +1) (D) 9 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) 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
20 m away from it with a angle of 30°. Find the the ground is 30°. After waling 50 3 toward
height of pole. the tower the angle becomes 60° height of the
tower is?
° °
3 °
(A) 20 3 m (B) 60 3 m
(A) 75 m (B) 65 3 m
40 3 100 3
(C) m (D) m (C) 90 3 m (D) 60 3 m
3 3
° °
(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) 60 m (B) 75 m
(A) 20 3 1 m (B) 40 3 1 m
(C) 30 m (D) 45 m
24. The angles of elevation of an aeroplane flying
(C) 10 3 m (D) 20 3 1 m
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?
° °
°
°
3 1 3 3
(A) (B)
2 2
200 3 200 3
(A) m (B) m (C) 3+ 3 (D)
3 1 3 1 3 +1
25. The tops of two poles of height 24 m and 36 m
300 3 300 3 are connected by a wire. If the wire makes an
(C) m (D) m
3 1 3 1 angle of 60° with the horizontal, then the
3 Maths By Adutiya Sir
length of the wire is
° °
°
20 3 1
(A) 8 3 m (B) 8 m (A) (B) 10
3
(C) 6 3 m (D) 6 m
20
(C) 10 3 (D) 3 1
26. An observer 1.6 m tall is 20 3 m away from a 3
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
3 above, at constant height then find the speed
° of zet plane.
P °
(A) 21.6 m (B) 23.2 m °
° °
(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
of the top of a tower is found to be such that
(C) 15 minutes 23 sec
8
(D) 17 minutes 23 sec tan A = . 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 3
another plane at an instant when the angle of such that tan B = . The height of the tower
4
elevation of two planes from the same point is-
on the ground are 60° and 45°, respectively.
Find the height of the lower plane from the
ground, in metres, is
8
tan A =
15
3
tan B =
4
° °
(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
the ground is 65 m. If the string makes an angle 44. A vertical stick 12 m long cast a shadow of 8 m
long on the ground. At the same time, a tower
12 cast a shadow of 40 m long on the ground. The
a° with the level ground such that a= , how
5 height of the tower is.
high is the kite?
12
a° a=
5
(A) 60 m (B) 65 m
x
(C) y (D) xy
5
x y h
9
4[( 3 ) – 1]
x °
60º 45º
(A) hcotx + h (B) hcotx – h
(C) htan – h (D) htanx – h
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
m. The angle of elevation of string with the (A) 193.22 (B) 144.04
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)
of the kite? 65. The angles of elevation of the top of a tower 72
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
P
6 P 450 3 (side) 60º 30º
60º 400 3
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
What will be the distance (in metres) between of their tops are 30º and 60º, respectively. The
two buildings? ratio of the height of P to that of Q is:
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)