The greatest cross track error acceptable is 5nm off the airway centreline.

We assume that the aircraft flies out of one beacon and then switches over half way to home to the next beacon so the greatest possible error will occur at the half way point.

The 1 in 60 rule can be used here.

Expressed as a formula it is:

 

distance off track   =          track error angle

distance gone                                  60

 

or,

 

distance gone                      =          distance off track x 60

                                                          track error angle

 

The maximum distance off track is 5nm, track error angle is 5.5º so

 

distance to half way          =          5 x 60 ÷ 5.5  =  54.5nm

 

distance between the beacons is twice that, 109 nm.