41)

What is the angle of elevation of the sun when the shadow of a 9-m high pole is \(3\sqrt 3\) m long?

SSC CGL 2022

A)

60°

B)

90°

C)

45°

D)

30°

42)

The tops of two poles of heights 18 m and 30.5 m are connected by a wire. If the wire makes an angle of 30° with the horizontal, what is the length (in m) of the wire?

SSC CGL 2022

A)

36

B)

28

C)

20

D)

25

43)

A and B are two points on the same side of a ground, 50 meters apart. The angles of elevation of these points to the top of a tree are 60° and 30, respectively. What is 40% of the height of the tree (in m)?

SSC CGL 2022

A)

\(10 \sqrt3\)

B)

\(15 \sqrt3\)

C)

\(25\sqrt{3}\)

D)

\(5 \sqrt3\)

44)

A ladder of length 3.5 m just reaches the top of a wall. If the ladder makes an angle of 60° with the wall, then what is the height of the wall (in m)?

SSC CGL 2022

A)

\(\frac{3.5}{\sqrt{3}}\)

B)

\(\frac{7 \sqrt{3}}{4}\)

C)

\(3.5 \sqrt{3}\)

D)

1.75

45)

From a ship's masthead 180 m high, the angle of depression of a boat is observed to be 60°. Find the distance (in m) of the boat from the ship.

SSC CGL 2022

A)

360

B)

\(60 \sqrt{3}\)

C)

\(180 \sqrt{3}\)

D)

180

46)

The length of the shadow of a vertical tower on level ground increases by 8.4 m when the altitude of the sun changes from 45° to 30°. What is the height of the tower (in m)?

SSC CGL 2022

A)

\(4.2( \sqrt 3 + 1)\)

B)

\(8.4( \sqrt 3 + 3)\)

C)

\(4.2( \sqrt 3 + 3)\)

D)

\(4.2( \sqrt 3 - 1)\)

47)

A ladder 18 m long 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)

\(18 \sqrt{3}\)

B)

9

C)

\(9 \sqrt{3}\)

D)

18

48)

A coconut tree swings with the wind in such a manner that the angle covered by its trunk is 18 degrees. If the topmost portion of the tree covers a distance of 44 metres,find the length of the tree.

SSC CGL 2022

A)

140 metres

B)

210 metres

C)

120 metres

D)

70 metres

49)

A person observes that the angle of elevation at the top of a pole of height 5 meters is 30°. Then the distance of the person from the pole is:

A)

5√3

B)

5/√3

C)

√3

D)

10√3

50)

The angle of elevation of the top of a tower from a point A on the ground is 30°. On moving a dis­tance of 20 metres towards the foot of the tower to a point B, the angle of elevation increases to 60°. The height of the tower is

A)

√3m

B)

5√3m

C)

10√3m

D)

20√3m