I'm currently editing some PowerPoint presentations for a scuba diving organization and have come across the word ascent several times; it brought to mind its homonym, assent, and led to today's post. :)
Ascent: an upward slope, or the act of moving upwards
Assent*: as a verb, to agree; as a noun, the act of agreeing
An easy way to remember the difference between these two is that in assent, the s's are the same—that is, they agree. Alternatively, in ascent, the s is farther "down" in the alphabet and it moves "up" to the c.
*Not related to the homonym aspect of the word, but still interesting, is Merriam-Webster's full definition of this word: agreeing to something "especially after thoughtful consideration." So, it would seem, to assent to something means not only to agree to something, but to do so after having thought the decision through thoroughly.