The distance between two pillars is 80 metres. The height of one pillar is twice of the other pillar. The angles of elevation of their top from the midpoint of the line connecting their feet arecomplementary to each other. The height of the big pillar is

In ∆ABP, tan θ = x/40 ……………. (i) In ∆ BCQ, tan (90 – θ) = 2x/40 Cot θ = 2x/40 ………. (ii) Multiplying both the equations, Tan θ. cot θ = x/40 × 2x/40 1 = x²/800 x² = 800 x = 20√2 Height of the big pillar = 2 × 20√2 = 40√2 m

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