ABCDEF is a regular polygon Two poles at C and D are standing vertically and subtend angles of eleva...........

Quantitative Aptitude (CDS) Mensuration 2D

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

1:1

$1:2\sqrt{3}$

$2\sqrt{3}:1$

$2:\sqrt{3}$

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Explanation:

∠ABC = 1200 [Angle of regular hexagon]
∠BAC = ∠BCA =(180⁰−120⁰)/2= 30⁰
∠DCA = 120⁰ – 30⁰ = 90⁰
Thus, $\Delta$ ADCA is a right triangle.
Let side DC = a

AC/a=cot30^o=AC=√3a
AD/a=cosec 30^o=>AD=2a
Now taking triangle ASD:
Let S is the vertex of pole

DS/AC=tan30^o=>DS=2√3
In triangle TCA:

TC/AC=tan30^o
=> TC =√3a /√3= a
Thus, ratio ∅
CT/DS=a/2√3a=1/2√3
Hence CT : DS = 1 : 2√3