PYQ Vault

Angles of elevation from two points are complementary: height squared = product of the distances

This type of question, asked 4 times: CDS 1 2019, CDS 1 2020, CDS 1 2024, CDS 2 2024. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2019

    34
    The angles of elevation of the tops of two pillars of heights hh and 2h2h from a point PP on the line joining the feet of the two pillars are complementary. If the distances of the foot of the pillars from the point PP are xx and yy respectively, then which one of the following is correct ?

    Tap an option to check your answer.

  2. Question 2

    CDS 1 2020

    57
    The angles of elevation of the top of a tower from two points at distances pp and qq from the base and on the same straight line are 27∘27^\circ and 63∘63^\circ respectively. What is the height of the tower?

    Tap an option to check your answer.

  3. Question 3

    CDS 1 2024

    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 ?

    Tap an option to check your answer.

  4. Question 4

    CDS 2 2024

    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 ?

    Tap an option to check your answer.