Canada ended a 22-year losing streak against Germany on Tuesday with Melissa Tancredi scoring both goals in a 2-1 win in Olympic women’s soccer action.
Great Britain did not enter a football team in the Olympics for the rest of the 1970s, plus the entire 1980s, 1990s and 2000s.
On 24 August 2008, British Prime Minister Gordon Brown suggested that the presence of a GB team at the 2012 games was "vital".
ET against Sweden, which defeated Brazil 1-0 in a penalty shootout in Tuesday's other semifinal.
The Canadians and Brazilians will meet in Friday's bronze-medal match at noon ET (watch live on cbc.ca/olympics, the CBC Rio 2016 app and on CBC TV).
South Africa's first shot on goal came from Andisiwe Mgcoyi, in the 21st minute, but it was easily saved by Karina Le Blanc.
Missed opportunities Banyana worked their way into the game and missed a couple of opportunities as they held off the world's seventh-ranked side.
Three minutes later, however, Sinclair fired home off her own rebounded shot, and Mndaweni was left stranded.
It was Sinclair again who beat the offside trap and, with only the keeper to challenge her, she slotted home her second and Canada's third goal in the 86th minute.
Poor defence by the South Africans saw Melissa Tancredi score her second goal of the tournament, from a Diana Matheson cross, in the seventh minute.
Banyana keeper Thokozile Mndaweni was forced to make a number of early saves as Matheson, Rhian Wilkinson and Kaylyn Kyle constantly troubled the defence.
The 10th-ranked Canadian women will play the runner-up in Group G in Friday’s quarter-final in Sao Paulo.