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Q.

The tops of two poles of height 18 m and 12 m are connected by a rope.  If the rope makes an angle 30°, with the horizontal.  If the length of the rope is 3l m, then l= _____

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answer is 4.

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Detailed Solution

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AB=18 m, CD=12 m, AE=18−12=6 m

Let BD=x, AC=3 l

Given ∠ACE=30°

In ΔAEC,

sin30°=6AC⇒12=6AC⇒AC=12

⇒AC=12=3×l (given)

∴l=4

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