Great Inagua is the third largest island in the Bahamas at 596 square miles ( 1544 kmÂ ) and lies about 55 miles ( 90 km ) from the eastern tip of Cuba . Great Inagua is the third largest island in The Bahamas at 596 sq mi ( 1544 kmÂ ) and lies about 55 miles ( 90 km ) from the eastern tip of Cuba .