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From a raised point, angles to the top and to the foot of a tower or tree: find its height

This type of question, asked 4 times: CDS 1 2017, CDS 1 2023, CDS 1 2025, CDS 2 2026. All 4 questions below, oldest first.

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  1. Question 1

    CDS 1 2017

    69
    From the top of a building 90 m high, the angles of depression of the top and the bottom of a tree are 30∘30^\circ and 45∘45^\circ respectively. What is the height of the tree ?

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  2. Question 2

    CDS 1 2023

    55
    A woman is standing on the deck of a ship, which is hh (in metres) above water level. She observes the angle of elevation of the top of a tower as 60∘60^\circ and the angle of depression of the base of the tower as 30∘30^\circ. What is the height of the tower ?

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  3. Question 3

    CDS 1 2025

    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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  4. Question 4

    CDS 2 2026

    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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