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Tower or pole at the centre of a square field: relate its height to the side

This type of question, asked 2 times: CDS 1 2018, CDS 1 2023. All 2 questions below, oldest first.

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  1. Question 1

    CDS 1 2018

    58
    Each side of a square subtends an angle of 60∘60^\circ at the tip of a tower of height h metres standing at the centre of the square. If ll is the length of each side of the square, then what is h2h^2 equal to ?

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  2. Question 2

    CDS 1 2023

    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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