What type of hat is this known as?
A trilby is a narrow-brimmed type of hat. The trilby was once viewed as the rich man's favored hat; it is sometimes called the "brown trilby" in Britain and was frequently seen at the horse races.
The traditional London hat company Lock and Co. describes the trilby as having a "shorter brim which is angled down at the front and slightly turned up at the back" versus the fedora's "wider brim which is more level". The trilby also has a slightly shorter crown than a typical fedora design.
The hat's name derives from the stage adaptation of George du Maurier's 1894 novel 'Trilby'. The trilby was also worn in the first London production of the play, and promptly came to be called "a Trilby hat". Its shape somewhat resembles the Tyrolean hat.
The hat reached its zenith of common popularity in the 1960s; the lower head clearance in American automobiles made it impractical to wear a hat with a tall crown while driving. It faded from popularity in the 1970s when any type of men's headwear went out of fashion, and men's fashion instead began focusing on highly maintained hairstyles.
Frank Sinatra was identified with trilby hats, and there is a signature design trilby bearing his name. Peter Sellers as 'Inspector Clouseau' wore a Herbert Johnson trilby in Blake Edwards's 'A Shot in the Dark' (1964), the second of his Pink Panther-series; the felt trilby giving way to a tweed one in later films. Trilby hats are worn by both men and women today.