lowest altitude of Alkaid?

Can anyone help me with this question?
I need to calculate the lowest altitude of Alkaid at my latitude which is
55
deg 45.9'

I found a formula for calculating the altitude at meridian transit facing
south but not sure if I can use it to calculate the altitude looking
directly north.

The formula was
objects altitude = (90 - observers latitude) + stars declination
This works out as
(90° - 55° 45.9') + 49° 18.795'
= 83° 32.895'
Obviously this is for transit of the observers meridian looking south


I modified the formula to
objects altitude = stars declination - (90 - observers latitude)
Because it appears to give me the correct answer (15° 4.695' ) but i'm not
sure its right and im having trouble getting my head round it lol

Does it look right?
comments?