[correct, morally correct, direct] Old English riht, of actions, "just, good, fair, in conformity with moral law; proper, fitting, according to standard; rightful, legitimate, lawful; correct in belief, orthodox;" of persons or their characters, "disposed to do what is good or just;" also literal, "straight, not bent; direct, being the shortest course; erect," from Proto-Germanic *rehtan (source also of Old Frisian riucht "right," Old Saxon reht, Middle Dutch and Dutch recht, Old High German reht, German recht, Old Norse rettr, Gothic raihts), from PIE root *reg- "move in a straight line," also "to rule, to lead straight, to put right" (source also of Greek orektos "stretched out, upright;" Latin rectus "straight, right;" Old Persian rasta- "straight; right," aršta- "rectitude;" Old Irish recht "law;" Welsh rhaith, Breton reiz "just, righteous, wise").
Compare slang straight (adj.1) "honest, morally upright," and Latin rectus "right," literally "straight," Lithuanian teisus "right, true," literally "straight." Greek dikaios "just" (in the moral and legal sense) is from dike "custom."
By 1580s as "in conformity with truth, fact, or reason; correct, not erroneous;" of persons, "thinking or acting in accordance with truth or the facts of the case," 1590s. Of solid figures, "having the base at right angle with the axis," 1670s. The sense of "leading in the proper or desired direction" is by 1814. As an emphatic, meaning "you are right," it is recorded from 1580s; use as a question meaning "am I not right?" is by 1961. Extended colloquial form righto is attested by 1896.
The sense in right whale (by 1733) is said in dictionaries to be "justly entitled to the name" (a sense that goes back to Old English); earliest sources for the term, in New England whaling publications, list it first among whales and compare the others to it. Of persons who are socially acceptable and potentially influential (the right people) by 1842.
Right stuff "best human ingredients" is from 1848, popularized by Tom Wolfe's 1979 book about the first astronauts. Right angle is from late 14c. The right way originally was "the way of moral righteousness, the path to salvation" (Old English); the sense of "correct method, what is most conducive to the end in vision" is by 1560s. The sense in in one's right mind is of "mentally normal or sound" (1660s).