1)

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

2)

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

3)

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

4)

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)

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

5)

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

6)

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

7)

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?

SSC CGL 2022

A)

115

B)

220

C)

330

D)

110

8)

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)

\(84\sqrt 3\)

9)

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:

SSC CGL 2022

A)

\(150\sqrt{3}\)

B)

\(85\sqrt{3}\)

C)

85

D)

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

10)

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?

SSC CGL 2022

A)

60°

B)

45°

C)

30°

D)

90°