For your method to work, you must make two points: one when you're exactly perpendicular to the ship's course, and one whenever you like. This gives a right-angled triangle. From there, you can caculate the distance travelled using Pythagoras' Theorem.
Exempli gratia
:
(You MUST remain still)
First point, you are 4km from the contact, bearing perpendicular to the course.
Second one, the contact is 5km away.
AB^2 + AC^2 = BC^2
4^2 + AC^2 = 5^2
16 + AC^2 = 25 [-16]
AC^2 = 9 [Square root]
AC = 3km
Now, we'll convert to knots later. Let's say it took 6 minutes ie. 0.1 hours.
=) S = d/t
S = 3/0.1
S = 30 km/h
Conversion to knots is km/h x 0.5399568 (0.5)
Therefore, the target is travelling at ~15 knots. Of course, the number's will never be this neat, so just round up; after all, nothing's perfect.
