The rule '1 in 60' 
Whenever you are aiming by vectors to 'send' an aircraft to a certain point  at no wind  there is a very simple rule that can suggest the vectoring angle . This simple rule under the easy name
'1 in 60'
replaces the trigonometric result at an accuracy of
98% !! It suggests that :
In
a distance of S=60 nm from a point , the deviation produced D , abeam that
point, equals
in nm the value of the angle in degrees
This simple rule is the basis for any vectoring
action , although it is not the only one to consider on using radar service
A Mathematical study
As
suggested simply by the following drawing the tangent of the angle a
equals the ratio D/S :
If x= arc in radians then every tangent may be analysed in series according to :
tanx = x + x^{2 }+ x^{3} +.....
To covert angle (a) in degrees we multiply by p/180 = 3.14/180 = 0.0174 which gives :
D = S * tan(a) = 60 nm * tan(a) , or after expanding tan(a) in powers :
D = (60 nm)* tan(a)= (60 nm) * [ 0.0174a + 0.0174^{2 + }0.0174^{3 }+ .....)]
the term 0.0174^{2} (something like 0.000302) and all the rest of its other powers are so small that practically 'kill' any such value for any 0<a<p/2 0 . This is why practically :
D = (60 nm ) * tan(a in degrees)=60 * 0.0174 nm = 1.044a nm , practically = 1a nm = a nm
In a distance of 60 nm you create a track deviation of 1 nm for every 1 degree of vectoring angle
What if
S
is not 60 nm ?
For any S<>60 nm , the deviation D is simply proportional as compared with 60 . If you vector from a closer than 60 nm distance you need to apply a larger angle to achieve the same deviation. Obviously ther opposite is true when you start from longer distances than 60 nm. In general , controllers prefer to aim from distances where the effect can be quickly assessed and this is better achieved in distances around 40 to 20 nm away from a point. Additionally they rarely consider deviation angles of less than 5 degrees as impractical for judgment. However, and despite any 'sacred rules' one may believe in, any combinations can be used under particular circumstances. Not all situattions are similar ; it is only the '1 in 60' rule that does not change !
So for any other Distance that is not 60 nm, the equivalent vectoring angle in degrees to achieve a certain Deviation , is :
vectoring angle = [60/Distance]*Deviation , in degrees

Example 1: At 40 NM from a point an aircraft wants to deviate 20 NM to the left to avoid an area around that point. What should be the vectoring angle ?
Answer : Distance = 40 nm , Deviation = 20 nm and deviation angle = (60/40)*20 = 30 degrees
Example 2: At 80 NM from a conflicting point we want to put an aircraft at a deviation of 10 nm . What should be the vectoring angle ?
Answer : Distance = 80 nm , Deviation = 10 nm and deviation angle = (60/80)*10 = 7.5 degrees , which suggests the more reasonable value for an instruction of 8 degrees