As
the feature is on a bearing of 270 relative to the aircraft imagine you are
heading due North.
3
minutes later it is at 315, so in effect a 45degree angle.
You
are heading North in calm conditions for 3 minutes at 180 knots which equates
to a distance of 9Nm.
Imagine
your start point which has a side length to the next point of 9Nm, as it was
due west at the beginning you have a 90 degree angle and then a 45 degree angle
creating a third angle of 45 (as a triangle is 180).
As
an isosceles triangle it will have 2 equal sides which are both 9Nm.
The
question asks for the minimum distance from the object which is indeed 9. The
length of the 3rd side is just over 12!