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Angle of elevation (or depression) from two points on the same side of a tower: find the height, distance or time

This type of question, asked 5 times: CDS 2 2016, CDS 1 2022, CDS 1 2023, CDS 1 2026, CDS 2 2026. All 5 questions below, oldest first.

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  1. Question 1

    CDS 2 2016

    73
    A man from the top of a 100 m high tower sees a car moving towards the tower at an angle of depression 30∘30^\circ. After some time, the angle of depression becomes 60∘60^\circ. What is the distance travelled by the car during this time ?

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  2. Question 2

    CDS 1 2022

    54
    The angle of elevation of the top of a tower of height xx metre from a point on the ground is found to be 60∘60^\circ. By going yy metre away from that point, it becomes 30∘30^\circ. Which one of the following relations is correct?

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  3. Question 3

    CDS 1 2023

    54
    A person on the top of a vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 6 minutes for the angle of depression to change from 30∘30^\circ to 45∘45^\circ, and further tt minutes to reach the tower, which one of the following is correct ?

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  4. Question 4

    CDS 1 2026

    44
    At a point on level ground, the tangent of the angle of elevation of the top of a tower is found to be 56\frac{5}{6}. On walking 70 m towards the tower, the tangent of the angle of elevation of the top of the tower is found to be 98\frac{9}{8}. What is the height of the tower ?

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  5. Question 5

    CDS 2 2026

    44
    A person walking along a straight road observes that at two consecutive kilometer-stones the angles of elevation of a hill in front of him are 30∘30^\circ and 60∘60^\circ respectively. What is the height of the hill ?

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