1. The angle of elevation of the top of a pillar from the foot and the top of a building 20 m high, are 60° and 30° respectively. The height of the pillar is
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By: anil on 05 May 2019 01.50 am
CE is the building = 20 m and BD = CE = 20 m AD is the pillar = ? Let AB = $$x$$ m and DE = BC = $$y$$ m Also, $$angle$$ AED = 60° and $$angle$$ ACB = 30° In $$ riangle$$ ADE, => $$tan(angle AED)=frac{AD}{DE}$$ => $$tan(60)=sqrt{3}=frac{x+20}{y}$$ => $$x+20=ysqrt{3}$$ --------------(i) In $$ riangle$$ ABC, => $$tan(angle ACB)=frac{AB}{BC}$$ => $$tan(30)=frac{1}{sqrt{3}}=frac{x}{y}$$ => $$y=xsqrt3$$ Substituting it in equation (i), we get : => $$x+20=(xsqrt{3}) imes sqrt3$$ => $$x+20=3x$$ => $$3x-x=2x=20$$ => $$x=frac{20}{2}=10$$ m $$ herefore$$ AD = AB + BD = 10 + 20 = 30 m => Ans - (D)
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