A person standing between two posts finds that angle subtended at his eyes by the tops of the post is right angle.If height of the post is two times and four times , the height of the person and distance between two post is equal to the length of the longer post. Find the ratio of distance of the person from shorter to longer post.

A person standing between two posts finds that angle subtended at his

1.	A person standing between two posts finds that angle subtended at his eyes by the tops of the post is right angle.If height of the post is two times and four times , the height of the person and distance between two post is equal to the length of the longer post. Find the ratio of distance of the person from shorter to longer post.
Answer» `In/_DCH` `tantheta=(DH)/(HC)=h/x` `h/x=tantheta-(1)` `In/_BCG` `tan(90-theta)=(BG)/(GC)` `cottheta=(3h)/(4h-x)-(2)` from equation 1 and 2 `(3h)/(4h-x)=x/h` `x^2-4hx+3h^2=0` `x^2-3hx-hx+3h^2=0` `x(x-3h)-h(x-3h)=0` `x=h,3h` When x=h `AF=4h-x=4h-h=3h` `FE=x=h` Ratio`=(EF)/(AF)=h/(3h)=1/3` Ratio=1/3.

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