Question

A person standing between 2 poles, finds that the angle subtended at his eyes by the top of the poles is a right angle. if the heights of the 2 poles are 2 times and 4 times the height of the person and the distance between the 2 poles is equal to the height of the higher pole. find the ratio of the distances of the person from the smaller to the bigger poles. (Plz give a reasonable answer and dont comment unnecessarily.... need a proper answer)

Answer 1

Now as the distance between two posts is given  ∴m+n=4x.............(1) Let ∠CPF =θ Now ∠APE+∠APC+∠CPF=180°(as EF is a straight line) ⇒∠APE+90°+θ=180° ⇒∠APE=180°−(90°+θ) =90°−θ  in ∆AEP,   tan(90°−θ) =AE.EP=xm ⇒cotθ=xm⇒tanθ=mx...........(2) Now in ∆CPF,tanθ =CF.PF=3xn......(3) From (2) and (3) mx=3xn⇒mn=3x2............(4) From  (1) and (4) we get,   m(4x−m) =3x2 ⇒m2−4mx+3x2=0 ⇒(m−3x)(m−x)=0 ⇒m=3x or m=x Hence n=4x−3x=x or n=3x ∴mn=3xx=31 ormn=x3x= 13So  m:n =3:1 or 1:3