The angle of elevation of the top of a tower from a point A on the ground is 30˚. On moving a distance of 20 metres towards the foot of the tower to a point B, the angle of elevation increases to 60˚. The height of the tower in metres is ?->(Show Answer!)

1. The angle of elevation of the top of a tower from a point A on the ground is 30˚. On moving a distance of 20 metres towards the foot of the tower to a point B, the angle of elevation increases to 60˚. The height of the tower in metres is

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By: anil on 05 May 2019 01.49 am

Given : CD is the tower and AB = 20 m To find : CD = $$h$$ = ? Solution : Let DB = $$x$$ m In $$ riangle$$ BCD, => $$tan(60^circ)=frac{CD}{DB}$$ => $$sqrt{3}=frac{h}{x}$$ => $$x=frac{h}{sqrt{3}}$$ -----------(i) Again, in $$ riangle$$ ACD, => $$tan(30^circ)=frac{CD}{AD}$$ => $$frac{1}{sqrt{3}}=frac{h}{x+20}$$ => $$x+20=sqrt{3}h$$ Substituting value of $$x$$ from equation (i), we get : => $$sqrt{3}h-frac{h}{sqrt{3}}=20$$ => $$frac{2h}{sqrt{3}}=20$$ => $$h=20 imes frac{sqrt{3}}{2}$$ => $$h=10sqrt{3}$$ m => Ans - (C)

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