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Question
Two poles of heights 25 m and 35 m stand vertically on the ground. The tops of two poles are connected by a wire, which is inclined to the horizontal at an angle of 30°. Find the length of the wire and the distance between the poles.
Solution
Let AC and BD are the two poles with heights of 25 m and 35 m, respectively.
Draw a horizontal line from point C to the line BD, and it meets BD at E (say).
∴ DE = 35 – 25 = 10 m
In ΔCDE, tan 30° = `("DE")/("CE")`
⇒ `1/sqrt(3) = 10/("CE")`
⇒ CE = `10sqrt(3)` m
Thus, distance between the poles = BA = CE = `10sqrt(3)` m
Again, In ΔCDE, sin 30° = `("DE")/("CD")`
⇒ `1/2 = 10/("CD")`
⇒ CD = 20 m
Hence, length of the wire is 20 m.
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