51)

The angle of elevation of the top of a tower from the point P and Q at a distance of 'a' and 'b' respectively from the base of the tower and in the same straight line with it are complementary. The height of the tower is:

A)

√ab

B)

a/b

C)

ab

D)

a²b²

52)

A tower standing on a horizontal plane subtends a certain angle at a point 160 m apart from the foot of the tower. On advancing 100 m to­wards it, the tower is found to sub­tend an angle twice as before. The height of the tower is

A)

80m

B)

200m

C)

100m

D)

160m

53)

At a point on a horizontal line through the base of a monument, the angle of elevation of the top of the monument is found to be such that its tangent is 1/5 . On walking 138 meters towards the monument the secant of the angle of elevation is found to be √193/12. The height of the monument (in metre) is

A)

42

B)

49

C)

35

D)

56

54)

A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30°. The man walks some distance to­wards the tower and then his angle of elevation of the top of the tower is 60°. If the height of tower is 30m, then the distance he moves is

A)

22m

B)

22√3m

C)

20m

D)

20√3m

55)

From two points on the ground lying on a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distance of the two points from the foot of the pillar are 9 metres and 16 metres and the two points lie on the same side of the pillar . Then the height of the pillar is

A)

5m

B)

10m

C)

9m

D)

12m

56)

The angle of elevation of the top of a chimney and roof of the building from a point on the ground are x and 45° respectively. The height of buidling is h metre. Then the height of the chimney,(in metre) is

A)

h cot x + h

B)

h cot x - h

C)

h tan x - h

D)

h tan x + h

57)

From a point P on the ground, the angle of elevation of the top of a 10m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff (Take √3 = 1.732)

A)

17.32m

B)

7.32m

C)

1.32m

D)

5.32m

58)

An aeroplane when flying at a height of 5000 m from the ground passes vertically above another aeroplane at an instant, when the angles of elevation of the two aeroplanes from the same point on the ground are 60° and 45° respectively, the vertical distance between the aeroplanes at that instant is:

A)

5000 (√3 - 1) m

B)

5000 (3 - √3) m

C)

5000 (\(1-{1 \over {\sqrt{3}}}\)) m

D)

4500 m

59)

The angle of elevation of an aeroplane from point A on the ground is 60°. After flight of 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of 1500√3 m, find the speed of the plane in km/hr.

A)

720 km/hr

B)

900 km/hr

C)

1000 km/hr

D)

1200 km/hr

60)

A vertical post 15 ft. high is broken at a certain height and its upper part, not completely separated meets the ground at an angle of 30°. Find the height at which the post is broken

A)

10 ft.

B)

5 ft.

C)

15 ft.

D)

20 ft.