The original problem is here. Exercise by Brian O'Connor
The problem was to locate your approximate position on a map after having taken a bearing of Eagle Mountain (13 degrees) and another of Fiddler mountain (92 degrees).
To start the process, you'd set your compass to 13 degrees (Eagle Mountain). Secondly, you'd align the north south lines in the compass's capsule with the north south UTM lines of the map with the direction of travel line aimed towards the north edge of the map. Third, you'd run the compass up or down the map until Eagle Mountain was on one of the compass's edges. Your location would be somewhere along that line.
Then, you'd repeat the sequence for Fiddler Mountain: dial in 92 degrees, align capsule's N/S lines with those of map with direction of travel line pointed generally towards the west map border, and slide the compass up or down the map until one of its edges intersected Fiddler Mountain. Your position would be somewhere along that line, and your best guess would be where the two lines intersect. This process is called rectification; it is more important to know how to do it than it is to remember the term.
Given the 1:100,000 scale of the blog map and the difficulty of dealing with a computer monitor, this was a challenging exercise, and it's hard to be absolutely precise. But you certainly should be able to place yourself somewhere in the ball park. If, for example, you'd been on the trail (to your east) and gotten off it and didn't know where it was, east or west of you, you could easily find it by using this technique on a paper map.
By my reckoning (and your mileage may differ a bit) the lines intersect at roughly:
In this problem, I wanted you to notice that other than orienting the map in order to properly identify the landmarks (Eagle Mountain and Fiddler Mountain), you didn't need to worry about either the orientation of the map or the compass's magnetic needle. Once you'd dialed in the bearing of the two landmarks, you were simply using your compass as a protractor.
Again, you can click on the map to enlarge it and then click on the magnifying glass icon for additional image boost. You should be near a summit and a bit left of the dotted line trail.