Tri tip pieces are typically served fairly thin. An ideal slice is around ¼ of an inch.  If you want to use the meat for sandwiches, the thinner the better. It can be difficult to cut really thin pieces from a hot roast without a meat slicer. Chilling the roast and slicing it cold makes it much easier to get really thin slices by hand. Reheat tri tip sliced for sandwiches in hot beef broth.