Uplanned diversions
Redout
You have been given good advice. Two additional points that I would make is;
The distance calculation isn't really necessary. The only measurement of value once airbourne, is time. I would spend my efforts in estimating elapsed time for the diversion based on the previous known progress on the already flown legs. Together with track made good assesment, at a predetermined pinpoint along the way, the time will also be revised. The Examiner will not expect a final heading or eta to be given until you have been able to revise based on a fix (pinpoint) along the way.
Don't rush to divert, identify a point ahead of your track, say 5 minutes of flying time to allow unrushed inflight planning. You should then consider other factors such as a MATZ and notified airspace which must be avoided. Where you may need to transit a MATZ or controlled airspace diverting from a point somw minutes ahead on your track will allow you time to gain clearances etc.