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Regular hexagon with poles at two vertices seen from vertex A: find the ratio of the pole heights

The same question, asked 2 times: CDS 1 2017*, CDS 2 2019. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2017

    80
    ABCDEF is a regular polygon. Two poles at C and D are standing vertically and subtend angles of elevation 30∘30^\circ and 60∘60^\circ at A respectively. What is the ratio of the height of the pole at C to that of the pole at D ?

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  2. Question 2

    CDS 2 2019

    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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