Beechjet 400
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 9
Distraction; Situational Awareness
ATC Issue All Types; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued New Clearance; General Flight Cancelled / Delayed
Chart Or Publication; Human Factors; Airspace Structure; Procedure
I was working an approach sector. I had a BE40 inbound on vectors to final. I had delay vectored him to get two slow Cessna aircraft in to the airport. At that time I also had a military aircraft inbound with minimum fuel that wouldn't take a speed reduction and also stated he couldn't take a very long downwind for fuel. I vectored the BE40 through final and then to a crosswind heading to delay for the military aircraft. Another aircraft was behind the BE40 that was kept inbound to follow the military aircraft. I went to coordinate the minimum fuel and no delay with Tower and realized that the BE40 hadn't been turned back to downwind and was about to enter a higher 9;600 ft. MVA while being at 9;000 ft. I hung up with Tower and instructed the BE40 to turn left to a heading of 300 and climb immediately to 9;600 ft. He entered the MVA block at 9;100 ft. climbing to 9;600 ft within 1 mile of the MVA boundary. I would recommend looking over my traffic next time before coordinating with Tower to make sure everything was separated to not be distracted while in communication with them.
Approach Controller reported vectoring an aircraft off the final approach course for sequencing placing it below the MVA.