Directions:

Two pillars P₁ and P₂ of equal heights stand on either side of a road which is 100 m wide. At a point on the road between the pillars, the angles of elevation of the tops of the pillars P₁ and P₂ are 60° and 30° respectively.

Based on this information, answer the following questions:

30. The height of each pillar is:
(a) 25 m
(b) 36 m
(c) $25\sqrt{3}$ m
(d) $36\sqrt{3}$ m

31. The location of the point of observation is:
(a) 25 m from P₁
(b) 25 m from P₂
(c) $25\sqrt{3}$ m from P₁
(d) $25\sqrt{3}$ m from P₂

32. If a hook is fixed at the point of observation and strings are tied from the hook to the tops of both the towers, then the total length of string required is:
(a) 43.3 m
(b) 86.6 m
(c) 68.3 m
(d) 136.6 m

33. If a flagstaff is to be erected atop pillar P₂ such that the angle of elevation of its top from the point of observation is 45°, then the height of the flagstaff must be:
(a) $25\sqrt{3}$ m
(b) 50 m
(c) $25\sqrt{3}(\sqrt{3}-1)$ m
(d) $25(2-\sqrt{3})$ m

Directions:

The angle of elevation of the top of a building from the foot of a tower is 30°. The angle of elevation of the top of the tower from the foot of the building is 60°. The tower is 30 metres high.

Based on this information, answer the following questions:

34.The horizontal distance between the tower and the building is:
(a) 10 m
(b) 17.3 m
(c) 20 m
(d) 34.6 m

35.The height of the building is:
(a) 10 m
(b) $10\sqrt{3}$ m
(c) 15 m
(d) $15\sqrt{3}$ m

36. The straight line distance between the tops of the tower and the building is:
(a) $10\sqrt{3}$ m
(b) $10\sqrt{5}$ m
(c) $10\sqrt{7}$ m
(d) 30 m

37. A bird flew straight from the top of the tower to the foot of the building. What is the distance that the bird flew?
(a) 20 m
(b) 25 m
(c) $20\sqrt{3}$ m
(d) $20(\sqrt{3}-1)$ m

Directions :

A TV tower stands vertically on the bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°.

Based on this information, answer the following questions:

38.The height of the tower is:
(a) 10 m
(b) $10\sqrt{3}$ m
(c) 20 m
(d) $20\sqrt{3}$ m

39.The width of the canal is:
(a) 10 m
(b) $10\sqrt{3}$ m
(c) 20 m
(d) $20\sqrt{3}$ m

40.The straight line distances of the top of the tower from the two points of observation differ by:
(a) 7.32 m
(b) 14.64 m
(c) 17.32 m
(d) 20.64 m

41.How far away from the other bank must the point of observation be, so that the angle of elevation of the top of the tower is 45°? (a) 7.32 m
(b) 10 m
(c) 14.64 m
(d) 27.32 m

Assertion (A): When observer moves horizontally towards the base of the object, angle of elevation decreases.

Reason (R): The line joining the observer’s eye and the object is called the horizontal line.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false