Question

A passeger is 6km away from railways line if the two eailway satios a and b are each 10km from the passenger then the distance between the places is

Answer 1

Solution:
Given:                 /O\
                          /   I   \
                        /     I     \
                      /       I  C  \
               A    --------------    B      (rough diagram)(OCB,OCA & OAB are triangles)

Let  O be the point where the passenger is standing, A and B are the stations which are 10 km away from the passenger(AO=BO=10km).such that C is the railway line (OC=6km),.

then, according to pythagoras theorem,
                                $AC^2+OC^2=OA^2$
                                $AC^2+6^2=10^2$
                                $AC^2=10^2-6^2$
                                $AC^2=100-36$
                                $AC^2=64$
                                $AC=8km$

                                $AC+BC=AB$
                                $AC+AC=AB$
                                $2AC=AB$
                                $2(8)=AB$
                                $AB=16km$ 
                  ∴The distance between the two stations is 16km.