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): At some time of the day, the length of the shadow of a tower is equal to its height, then the sun’s altitude is 45°.

Reason (R): The angle which the line of sight makes with the horizontal line passing through the observer’s eye, when the object is above the observer, is called the angle of elevation.

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