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Heights and Distances

CDS Maths. Try each one first, then open its answer.

Top 10 CDS PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 5 times: CDS 2 2016, CDS 1 2022, CDS 1 2023, CDS 1 2026, CDS 2 2026. This one: CDS 2 2026 See all 5 of this type

    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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  2. Question 2

    This type asked 5 times: CDS 2 2016, CDS 1 2017, CDS 2 2021, CDS 2 2024, CDS 1 2026. This one: CDS 1 2026 See all 5 of this type

    45
    Two persons are on diametrically opposite sides of a tower. They measure the angles of elevation of the top of the tower as 30∘30^\circ and 60∘60^\circ respectively. If the height of the tower is 100 m, what is the approximate distance between the two persons ?

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  3. Question 3

    This type asked 4 times: CDS 1 2017, CDS 1 2023, CDS 1 2025, CDS 2 2026. This one: CDS 2 2026 See all 4 of this type

    45
    A tower subtends an angle α\alpha at a point P on the same level as the foot of the tower. Q is a point vertically above P and PQ = h. If the angle of depression of the foot of the tower measured from Q is β\beta, then what is the height of the tower ?

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  4. Question 4

    This type asked 4 times: CDS 1 2019, CDS 1 2020, CDS 1 2024, CDS 2 2024. This one: CDS 2 2024 See all 4 of this type

    46
    A vertical pole of length 80 m is situated on the horizontal plane. The base of the pole is at PP. There are two points AA and BB such that PP, AA, BB are on the same straight line. Let the angles of elevation of top of the pole from AA and BB be α\alpha and β\beta (α>β\alpha > \beta) respectively. If PA=64PA = 64 m and AB=36AB = 36 m, then what is (α+β)(\alpha + \beta) equal to ?

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  5. Question 5

    Asked 2 times: CDS 1 2017*, CDS 2 2019 (* = numbers or wording changed that year) See all 2 times it was asked

    54
    Consider a regular hexagon ABCDEF. Two towers are situated at B and C. The angle of elevation from A to the top of the tower at B is 30∘30^\circ, and the angle of elevation to the top of the tower at C is 45∘45^\circ. What is the ratio of the height of towers at B and C ?

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  6. Question 6

    This type asked 2 times: CDS 1 2018, CDS 1 2023. This one: CDS 1 2023 See all 2 of this type

    68
    ABCD is a square field with AB = x. A vertical pole OP of height 2x stands at the centre O of the square field. If ∠APO=θ\angle APO = \theta, then what is cot⁡θ\cot\theta equal to ?

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  7. Question 7

    Asked once: CDS 1 2026 (same type asked 5 times) See all 5 of this type

    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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  8. Question 8

    Asked once: CDS 2 2024 (same type asked 5 times) See all 5 of this type

    18
    From a point XX on a bridge across a river, the angles of depression of two points PP and QQ on the banks on opposite side of the river are α\alpha and β\beta respectively. If the point XX is at a height hh above the surface of the river, what is the width of the river if α\alpha and β\beta are complementary ?

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  9. Question 9

    Asked once: CDS 1 2025 (same type asked 4 times) See all 4 of this type

    25
    A tower subtends an angle 60∘60^\circ at a point A on the same level as the foot of the tower. B is a point vertically above A and AB = h. The angle of depression of the foot of the tower, measured from B is 30∘30^\circ. What is the height of the tower ?

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  10. Question 10

    Asked once: CDS 1 2024 (same type asked 4 times) See all 4 of this type

    53
    The angles of elevation of the top of a tower from two points A and B at a distance of x m and (x+5)(x + 5) m from the base of the tower of height 6 m and in the same straight line with it are complementary. What is the value of x ?

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