The Spanish word 'agudo' (meaning 'sharp' or 'acute') comes from the Latin word 'acutus' meaning 'sharp' or 'pointed'. This Latin word was derived from the verb 'acuere' meaning 'to sharpen', which in turn came from the Latin adjective 'acer' meaning 'sharp' or 'keen'. The evolution from Latin 'acutus' to Spanish 'agudo' shows a common sound change where the 'c' (pronounced like 'k') softened to 'g' between vowels, and the Latin ending '-us' evolved into '-o' as was common in the development of Spanish words from Latin.

Some related Spanish words include 'aguja' (needle), which also comes from Latin 'acus' (needle) and shares the same root relating to sharpness. The word 'aguijón' (stinger) is another related term that carries the basic meaning of something sharp or pointed.

Several English words are related to 'agudo' through the same Latin roots. The most obvious is 'acute', which comes directly from Latin 'acutus' and has similar meanings of 'sharp' both literally and figuratively. Other related English words include 'acerbic' (sharp or bitter in taste or manner) and 'acrid' (sharp or irritating), both of which derive from the same Latin root 'acer'.