Also useful for working out how many miles to fly around a DME arc procedure.
e.g. 12 dme arc (= 1/5 of 60)
If you are going to fly approximately 50 degrees of arc (you joined on the 295 radial, and your lead radial is 245 degrees from the beacon - you are flying south around the arc), then the distance on the arc will be about 10 miles. Gives you an idea how fast you can fly it, before slowing down and configuring for the turn inbound (some arcs are very much shorter of course).
Also can be used for working out how far off track you've deviated for weather avoidance or while on radar vectors, etc, as well as a whole heap of other things.