Hi Involute, you're welcome and I'm glad it passes now!
Later tonight I'll send some more details on how to fill the triangular area, but real quick for now the key thing is that it is done using an "untrim" followed by an Edit > Trim. There is some info on untrim here: http://moi3d.com/forum/index.php?webtag=MOI&msg=444.4 and also in the object repair tutorial here: http://www.moi3d.com/forum/index.php?webtag=MOI&msg=446.17
You have to use Edit > Separate on the "ground" face first to break it off into an individual surface, after that you can do the untrim by selecting all of its edges (quick way to select all edges of a surface is to select one edge to start with and then use Ctrl+A for "Select All") and hitting Delete. That will remove the trim boundaries and recover the full original "underlying surface" of the face which is a big sphere. Then it has to be retrimmed.
Also one other quick note for now - it looks like you put in a line here to make the new vertical plane:
That won't be quite right because the "ground" face is curved, so instead you want that new vertical plane to initially stick downwards a ways so it pushes through the ground then use Edit > Trim on it using the ground as the cutting object. Once you have trimmed that vertical plane with the ground you'll then have all the edges to retrim the ground sphere, there are 19 edges that the sphere needs to be trimmed against but they are all naked edges so in the Edit > Trim command you can use the "Select naked edges" shortcut key to select all the needed ones rather than going around and selecting them with individual clicks. Once the "ground" sphere is retrimmed you then use Edit > Join to glue it back in place.
I can give you some images later tonight to explain it better.
- Michael
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