You've only answered one part of the question.

Since no one seems willing to do this probably, here are the answers:
Starting with heading of 190 and speed through water 5, to have a COG of 90
and
SOG of 5,
current must be 50 degrees, speed of 7.66

Starting with heading of 190 and speed through water 5, to have a COG of 90
and
SOG of 2.5,
current must be 34.37 degrees, speed of 5.96



For any oblique triangle with angles A, B, and C, and opposite sides a,b,
and, c
then:
the law of sines says:

a/ sinA = b / sinB = c / sinC = diameter of circumscribed circle

and the law of cosines says:
c^2 = a^2 + b^2 - 2*a*b* cos C



"SkitchNYC" wrote in message
...
Say you are sailing a course of 190 and making 5 kn. An adverse current
suddenly gets you and you are now making a COG of 90. Assume the new COG
is
at
the same speed (5kn) and again at 2.5 kn. What direction and speed must
the
current be to produce either of these results? Can such a current exist in
a
Gulf Stream eddie?