PYQ Vault

Two points on opposite sides of a tower or below an observer: width = h(cot a + cot b)

This type of question, asked 5 times: CDS 2 2016, CDS 1 2017, CDS 2 2021, CDS 2 2024, CDS 1 2026. All 5 questions below, oldest first.

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  1. Question 1

    CDS 2 2016

    74
    Two men on either side of a tower 75 m high observe the angle of elevation of the top of the tower to be 30∘30^\circ and 60∘60^\circ. What is the distance between the two men ?

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  2. Question 2

    CDS 1 2017

    100
    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\alpha and β\beta. The height of the aeroplane above the road is

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  3. Question 3

    CDS 2 2021

    51
    From an aeroplane flying above a river at an altitude of 1200 m, it is observed that the angles of depression of opposite points on the two banks of a river are 30∘30^\circ and θ\theta. If the width of the river is 3000 m, then which one of the following is correct ?

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  4. Question 4

    CDS 2 2024

    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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  5. Question 5

    CDS 1 2026

    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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