HEIGHT AND DISTANCE (CDS)

Total Questions: 24

11. From an aeroplane vertically over a straight horizontal road, the angles of depression of two consecutive kilometre-stones on the opposite sides of the aeroplane are observed to be α and β. The height of the aeroplane above the road is [2017 (I) Morning Shift]

Correct Answer: (b)
Solution:

12. A man from the top of a 100 m high tower seen a car moving towards the tower at an angle of depression 30°. After some time, the angle of depression becomes 60°. What is the distance travelled by the car during this time? [2016 (II) Evening Shift ]

Correct Answer: (b) (200√3)/3 m
Solution:Let AB be the tower of height is100m.

13. Two men on either side of a tower 75 m high observed that the angle of elevation of the top of the tower to be 30° and 60°. What is the distance between the two men? [2016 (II) Evening Shift ]

Correct Answer: (a) 100√3 m
Solution:


14. If the length of the shadow of a tower is equal to its height, then what is the Sun’s altitude at that time? [2016 (II) Evening Shift ]

Correct Answer: (c) 45°
Solution:Let AB and BC be the height of tower and length of the shadow of a tower.

15. Two observers are stationed due North of a tower (of height x m) at a distance y m from each other. The angles of elevation of the tower observed by them are 30° and 45°, respectively. Then, x/y is equal to [2016 (I) Morning Shift]

Correct Answer: (c)
Solution:In right angled ∆ADC, tan45° = AC/CD

16. An aeroplane flying at a height of 3000 m passes vertically above another aeroplane at an instant, when the angles of elevation of the two planes from some point on the ground are 60° and 45°, respectively. Then, the vertical distance between the two planes is [2015 (II) Evening Shift ]

Correct Answer: (c) 1000 (3 - √3) m
Solution:Let A and B be the position of two planes and D be a point.

17. A pole is standing erect on the ground which is horizontal. The tip of the pole is tied tight with a rope of length √12 m to a point on the ground. If the rope is making 30° with the horizontal, then the height of the pole is [2015 (II) Evening Shift ]

Correct Answer: (d) √3m
Solution:AB is a pole and AC is rope. Let height of the pole AB = h

18. The angles of elevation of the top of a tower from two points P and Q at distance m² and n² respectively, from the base and in the same straight line with it are complementary. The height of the tower is [2015 (I) Morning Shift]

Correct Answer: (d) mn
Solution:Let the height of the tower be h. PB = m² and QB = n²


19. The angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. The height of the cloud is [2015 (I) Morning Shift]

Correct Answer: (c) 400 m
Solution:Let P be the cloud at height Habove the level of the water in the lake and Q its image in the water.


20. From the top of a tower, the angles of depression of two objects P and Q (situated on the ground on the same side of the tower) separated at a distance of 100 (3 - √3) m are 45° and 60°, respectively. The height of the tower is [2015 (I) Morning Shift]

Correct Answer: (c) 300 m
Solution:Let BC h = be height of tower and P and Q be the points, where the angle subtended are 45° and 60°. In right angled ∆BQC,