Eclipse 500
Air Traffic Control Fully Certified
Situational Awareness
Deviation - Speed All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance
Human Factors; Procedure
Aircraft X was the only aircraft being worked.  Just before or during the briefing the pilot had expressed concern about radar vectors to the ILS Z Runway 12 approach that they would be too short for his autopilot to take.  It struck me as strange because he was still on the downwind with approximately 15-20 miles to fly before base turn.  The pilot requested to start the approach from EMIBE; an IAF; which was behind him.  The Supervisor issued a vector 020 and told the aircraft to expect direct EMIBE once the intercept was less than 90 degrees.  I took the position; and was evaluating whether 020 would be enough of a turn.  Then the Supervisor keyed up the briefing button and briefed me on OSR (CIC) position.  I turned Aircraft X to H050; thinking the turn back to EMIBE from the 020 would be too tight.  By this point the aircraft had increased speed 50-60 kts.  I called ZLC Sector 19 with a point out since I knew he would be close to the airpsace boundary turning to EMIBE and cleared Aircraft X direct EMIBE; cross EMIBE at 10;000; cleared ILS Z Runway 12 approach.   The Supervisor and I watched as the aircraft got close to a 11;000 MVA; but it was obvious the aircraft would turn inside of it; and the Supervisor made a comment to that fact.  At this point the Supervisor left since their position overlap was complete.  After EMIBE; the pilot flew direct NEGOE instead of flying the DME arc on the approach.  I advised him of the course deviation; and said I could vector him outside of NEGOE or back to EMIBE; and he opted for vectors to final outside of NEGOE.  I cancelled their approach clearance and vectored them to final.  On their base to final turn Aircraft X gained approximately 80 kts of ground speed; and went through final; I gave them vectors to join from the other side.After getting off position I wanted to review the falcon replay because the aircraft got closer to the 11;000 MVA than I expected; and I wanted to review the situation.  During this time; I realized I had an error and the aircraft had entered a 10;600 MVA at 10;000; and flew in that MVA for several miles.  This happened before the aircraft neared the 110 MVA.  For some reason I did not consider that MVA; or recognize that Aircraft X would or had lost separation with terrain there.I recall at the time feeling that something [wasn't] right; but I attributed it to the pilot's request and concern about vectors to final.  It is unusual to vector an aircraft to EMIBE; and I may have cleared 5 or so aircraft at EMIBE in the last year.  The MVA immediately south of the 10;600 MVA is 8;000 feet; and immediately west is 8;600 feet.  The MVA map shows 10;600 at the far north of the map and far northeast; and I think I overlooked it as being part of the 8;600 MVA.  I distinctly remembered thinking he would be fine at 10;000 when I took the position; and my only concern was for the 11;000 MVA at the time.I would like to recommend that the MVA map (Fusion 3 mile map) be updated to add a 106 note just below the 110 MVA; which is at the southwest corner of the 106 MVA (the maps are abbreviated altitudes).  Most MVA altitudes on the map are near where the aircraft are being vectored; and I understand they are sparse to reduce clutter.  However; I think that might have helped me avoid this loss.Since learning of this error; I have spent some time looking at the terrain in detail (including google maps terrain); and realizing how close this aircraft was to terrain; and it has shocked me.  I wondered if the pilot was receiving any terrain warnings; but did not say anything.  I deeply regret that this happened and am glad that the pilot is ok.
GEG TRACON Controller reported  having to turn an aircraft on to final and realizing later that the aircraft was below the MVA.