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.

Answer 1

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.