71)

The tops of two poles of height 24 m and 36 m are connected by wire. If the wire makes an angle of 60° with the horizontal, then the length of the wire is. 

A)

8√3 m

B)

6√3 m

C)

8 m

D)

6 m

72)

From an aeroplane just over a river, trees on the opposite bank of the river are found to be 60° and 30° respectively. If the breadth of the river is 400 m, then the height of the airplane above the river at  an instant is 
(assume √3 = 1.732)

A)

173.2 m

B)

346.4 m

C)

519.6 m

D)

692.8 m

73)

There are two verticals posts, one on each side of a road, just opposite to each other.One post is 108 metre high. From the top of this post, the angles of depression of the top and foot of the other post are 30° and 60° respectively. The height of the other post, in metre is:

A)

36

B)

72

C)

108

D)

110

74)

There are two temples, one on each bank of a river just opposite to each other. One temple is 54 m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are 30° and 60° respectively. The height of the temple is

A)

18 m

B)

36 m

C)

18√3 m

D)

36√3 m

75)

The angle of elevation of the top of a vertical tower situated perpendicularly on a plane is observed as 60° from a point P on the same plane. From another point Q, 10 m vertically above the point P, the angle of depression of the foot of the tower is 30°. The height of the tower is

A)

15 m

B)

20 m

C)

25 m

D)

30 m

76)

A vertical pole and a vertical tower are standing on the same level ground. Height of the pole is 10 metres. From the top of the pole the angle of elevation of the top of the tower and angle of depres­sion of the foot of the tower are 60° and 30° respectively. The height of the tower is

A)

20 m

B)

30 m

C)

40 m

D)

50 m

77)

From the top of a tower of height 180 m the angles of depression of two objects on either sides of the tower are 30° and 45°. Then the distance between the objects are

A)

180 (3 + √3) m

B)

180 (3 - √3) m

C)

180 (√3 - 1) m

D)

180 (√3 + 1) m

78)

The distance between two parallel poles is 40√3 m. The angle of depression of the top of the second pole when seen from the top of first pole is 30°. What will be the height of second tower if the first pole is 100m long?

A)

50√3 m

B)

80 m

C)

35√3 m

D)

60 m

79)

From the top and bottom of a straight hill, the angle of depression and elevation of the top of a pillar of 10 m height are observed to be 60° and 30° respectively. The height (in metres) of the hill is

A)

30

B)

40

C)

60

D)

80

80)

The height of a house subtends a right angle at an opposite window & the line through the window to the top of the house makes an angle θ with the vertical. If the breath of the street be ‘d’ meters. Find the height of the house

A)

d.sinθ.cosθ

B)

d.sinθ.secθ

C)

d.secθ.cosecθ 

D)

d.cosθ.cosecθ