Usage patterns
〈人〉が投げを打つto execute a throw (in judo, sumo, etc.)
The athlete pulled off a beautiful throw and won the match.
投げを打つto resign (a game of shogi or go)
Seeing that the position was hopeless, he resigned the game.
投げが出るfor a sell-off/panic selling to occur in the market
The market plunged and a wave of panic selling followed.
Expressions
匙を投げるgive up as hopeless; throw in the towel