At LAN, the Sun is directly located along your Celestial Meridian, and it will be located at it's highest point for the day. At LAN, your LAT can be found by some combination of ZD (Zenith Distance) and DEC.

 

You can assume, and you will, that 90° (or 89°60' to make your calculations easier), 90° minus Ho gives you ZD. This is true because ZD is the distance from your Zenith to the body at the time of observation, and 90° would be the distance all the way to the horizon, so Ho is the distance leftover, or the distance from the body to the horizon.

 

When assumed Latitude and calculated Declination are Same Name, and Latitude is greater, ZD+Dec=Lat.

 

When aLAT and DEC are Contrary Name, Lat=ZD-Dec.

 

It always helps to draw out a picture like the ones at left whenever solving these types of problems.

To Put The Whole Process Simply:
-Calculate time of LAN early in the day to make sure you don't miss it
-Observe the sun's altitude with a sextant at LAN
-Reduce down your sight from Hs to Ho
-Calculate Dec of the sun at LAN
-Subtract Ho from 90° to find ZD, or from 89°60', which makes the calculations easier
-Calculate LAT using ZD and Dec. Draw a diagram to find which equation to use.