My goal is to digitize a scan and I'm struggling with creating smoothing corner and a triangle edge. Here is what I mean:

Right now I am attempting to use the "Edit paths by nodes (N)".  However, it is not working out that well especially with the hard edges at the top.

I'm thinking the next best attempts is to create two rectangles where one would be skewed.  After that create a circle and combine the rectangles with circle to come up with the desired image.

Would anyone have any other alternative methods for this?

It looks like you have a single path with some thickness to the stroke. That arrangement will never let you get the 'hard edge' you want on the right. Here's what I would do:

1. Using the node tool, double click on the line on either side of the corner node. You now have three nodes in this area.
2. Delete the middle node (the original corner node). This will give you a smooth path between the two remaining nodes.
3. Adjust the handles of the remaining nodes to get the curve looking the way you want.
4. Path > Stroke to Path.
5. Draw a rectangle over the top of the path, so that the lower edge of the rectangle marks the 'hard edge' you want.
6. Select both the rectangle and the path.
7. Path > Difference.

Note that the shape is now a filled path, not a stroked path, so if you do need to make other edits to it you'll need to take that into account.

@Xav  thank you so much.  I'm still working with it.  Trying to do more practice with "Draw Bezier curves and straight lines (B)", "Edit paths by nodes (N)", and "Document Properties"->"Grids"/"Snap to visible gridlines"/"Grid units"/"Grid units"/"Spacing X"/"Spacing Y".

It has been hard moving and adjusting nodes because of the mouse.  The grid lines need to be more fine and also don't match some of my measurements because they are in pixel.  Therefore I need to adjust some of this to get a very nice smooth in the middle.  

Also, need to learn how to better adjust that top edge.  Practice, practice, practice...