31)

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

32)

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)

\(84\sqrt 3\)

33)

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)

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

34)

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°

35)

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:

SSC CGL 2022

A)

1 : 3

B)

√3 : 1

C)

1 : √3

D)

3 : 1

36)

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?

SSC CGL 2022

A)

30

B)

25

C)

24

D)

27

37)

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?

SSC CGL 2022

A)

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

B)

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

C)

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

D)

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

38)

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).

SSC CGL 2022

A)

130

B)

195

C)

195√3

D)

65

39)

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?

SSC CGL 2022

A)

60

B)

30

C)

45

D)

15

40)

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?

SSC CGL 2022

A)

20

B)

20√3

C)

10√3

D)

10