21)

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

22)

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

23)

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:

SSC CPO 2020

A)

6.6 X √2

B)

3.3 X √2

C)

2.2 X √2

D)

3.6 X √2

24)

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:

SSC CPO 2020

A)

√3 : 1

B)

1 : 3

C)

1 : √3

D)

3 : 1

25)

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?

SSC CGL 2022

A)

52√3

B)

26√3

C)

80

D)

78√3

26)

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?

SSC CGL 2022

A)

22

B)

17

C)

39

D)

35

27)

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.

SSC CGL 2022

A)

38

B)

57

C)

19√3

D)

19

28)

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.

SSC CGL 2022

A)

45

B)

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

C)

180

D)

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

29)

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).

SSC CGL 2022

A)

72

B)

\(24(\sqrt3+1)\)

C)

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

D)

96

30)

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:

SSC CGL 2022

A)

80

B)

96

C)

84

D)

90