Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2016MathematicsHeights and Distances

From an aeroplane flying, vertically above a horizontal road, the angles of depression of two consecutive stones on the same side of the aeroplane are observed to be 30^ and 60^ respectively. The height at which the aeroplane is flying in km , is

Options

  1. A2
  2. B2 3
  3. C3 2
  4. D4 3

Correct answer

C. 3 2

Step-by-step solution

Let the distance of two consecutive stones are (x, x+1) . In B C D , we have 60^ = h x x= h 3 ...(i) In A B C , we have 30^ = h x+1 1 3 = h x+1 h 3 +1= 3 h [by Eq. (i)] array ll & h ( 3 - 1 3 )=1 & h ( 2 3 )=1 h= 3 2 array

Practice Heights and Distances on Quantrex Academy →

More from Heights and Distances

The lengths of the shadows of a tree of height p, thrown by sun's rays at three different moments are p, 2p and 3p. The sum of the angles of elevation of the sun's rays at these th 2026The horizontal distance between a tower and a builidng is 10 3 units. If the angle of depression of the foot of the building from the top of the tower is 60^ and the angle of eleva 2025An aeroplane is flying at a constant speed, parallel to the horizontal ground at a height of 5 kms. A person on the ground observed that the angle of elevation of the plane is chan 2025A ladder, 5 meters long; rests against a vertical wall. If its top slides downwards at the rate of 10 ~cm / s , then the angle between the ladder and the floor is decreasing at the 2023A ladder 5 meters long rests against a vertical wall. If its top slides downwards at the rate of 10 ~cm / s , then the angle between the ladder and the floor is decreasing at the r 2023A rod A B, 13 feet long moves with its ends A and B on two perpendicular lines O X and O Y respectively. When A is 5 feet from O , it is moving away at the rate of 3 feet / sec . A 2023A man (2 ~m ) tall, walks at the rate of (1 2 3 ~m / s ) towards a street light which is (5 1 3 ~m ) above the ground. The rate at which the length of his shadow is changing when h 2020A person standing on the top of a building of height 60 3 feet observed the top of a tower to lie at an elevation of 45 ° . That person descended to the bottom of the building 2020 Full Heights and Distances list All COMEDK PYQs