Dr. Winger stands on the drill field just north of President Lee's statue. He walks 20.0 m north on the sidewalk toward Lee Hall while thinking about going back to work. He then decides to go talk to his wife and cuts across the grass at an angle of 75 degrees south of east from 40.0 m heading towards the Library, but changes his mind again and walks towards the Union at an angle of 10 degrees north of west for 30.0 m hoping to get Starbuck's at the Union. Determine how far Dr. Winger is from where he started.