The angle of elevation of an aeroplane from a point on the ground is 45°. After 15 seconds of flight, the elevation changes to 30°. If the aeroplane is flying at a height of 3000 m, the speed of the plane in km per hour is:

1. 152.16

2. 263.5

3. 304.32

4. 527

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 :

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