Two Poles are 12 metres apart horizontally and the height of one is double that of the other. If from the mid-point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary. Then the height of the shorter post is:

Let AB = taller pole CD = shorter pole = h OB = OD =( 12)/2 = 6m In ∆OCD, tanθ = h/6 ............................(i) In ∆AOB tan (90- θ) = 2h/6 = h/3 cotθ= h/3 .............................(ii) Multiplying (i) and (ii), we get tanθ × cotθ = h/6 × 4/3 1 = h²/18 h² = 18 h=3√2 m

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