The words height, hight sound the same but have different meanings and spellings. Why do height, hight sound the same even though they are completely different words?
The answer is simple: height, hight are homophones of the English language.
The distance from the base of something to the top.
Elevation above a given level, as of the sun or a star above the horizon; altitude. See Synonyms at elevation.
The condition or attribute of being relatively or sufficiently high or tall.
Stature, especially of the human body.
Archaic Named or called.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.