NavList:

Hi Mark

"Exact" angular separation between Polaris and Merak will depend upon the initial set of coordinates.  To what resolution do you need the angular separation to be?  An arcminute?  An arcsecond? 

So rather than just give you an answer, I will give you the tools so that you can compute the distance on your own.  Naturally, I will provide an example with the equation.

First, find the Right Ascension and Declination of both objects.  I will use
Polaris
RA 2h 31m 52.051s
Dec N 89d 15m 50.64s
Merak
RA 11h 1m 50.52s
Dec N 56d 22m 57.00s

Since the h.m.s format is difficult to deal with, convert it to decimal.
Decimal RA=h+(m/60)+(s/3600k
Polaris
RA=2+31/60+52.051/3600
RA=2.5311252778
Merak
RA=11+1/60+50.52/3600
RA=11.0307

Also, convert the d.m.s format to decimal degrees
Decimal Declination=d+(m/60)+(s/3600)
Polaris
Dec=89+15/60+50.64/3600
Dec=89.2640666667
Merak
Dec=56+22/60+57.00/3600
Dec=56.3825

You will need to convert RA to Sidereal Hour Angle.  SHA=360d-(RA*15d/h).
Polaris
SHA=360-( 2.5311252778*15)
SHA=322.0331208333
Merak
SHA=360-( 11.0307*15)
SHA=194.5359 

The angular separation between the two bodies is then given by

arccos(sin(dec1)*sin(dec2)+cos(dec1)*cos(dec2)*cos(SHA1-SHA2))

arccos(sin( 89.2640666667)*sin( 56.3825)+cos(89.2640666667)*cos( 56.3825)*cos( 322.0331208333-194.5359))

arccos(.8283548032)

34.069894429 Degrees

or

34 Deg 4 min 11.62 sec

THIS DOES NOT ACCOUNT FOR REFRACTION.

Now you have the keys to compute the distance between any two stars.

Regards
Brad