Ian is 5.4 feet tall and touches the ceiling when he is standing 4.2 feet from the edge of the attic. The distance from the edge to the center of the attic is 9 feet. What is the height of the ceiling at the highest point?

1 Answer
Mar 11, 2018

drawn

Situation as described in the problem has been shown i above figure where

  • #AB=hft->#height of the ceiling at the highest point

  • #DE=5.4ft->#height of Ian.

  • #CB=9ft-># the distance from the edge to the center of the attic .

  • #CD=4.2ft-># the distance of Ian from the edge of the attic (C).

It is obvious that the #DeltasABC and EDC# are similar

So we have

#(AB)/(DE)=(BC)/(CD)#

#=>h/5.4=9/4.2#

#=>h~~11.57 ft#