The distance between two pillars is 120 metres. The height

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The distance between two pillars is 120 metres. The height of one pillar is thrice the other. The angles of elevation of their tops from the mid point of the line connecting their feet are complementary to each other. The height (in metres) of the taller pillar is (Use : √3 = 1.732)

Let, AB = 3h metre
CD = h metre
BE = ED = 60° metre
∠AEB = 90° – θ ; ∠CED = θ
In ∆ABE,

tan (90° – θ) =	AB
	BE

⇒ cot θ =	3h	.......(i)
	60

In ∆CED,

tan θ =	h	.......(ii)
	60

∴ tanθ . cotθ =	3h	×	h
	60		60

⇒ 3h² = 60 × 60

⇒ h² =	60 × 60	= 1200
	3

⇒ h = √1200
= 20 √3 metre
∴ Height of larger pole
= 3 × 20 √3 = 60 √3 metre
= (60 × 1.732) metre
= 103.92 metre