Question

What is an example of appeal to ethos?

Answer 1

Appealing to ethos is like "resting on your laurels," or using your credentials/authority/experience/character/age/wisdom as the backing for your argument. Examples:

-"As a distinguished professor, I don't think you should try to submit your paper to that publication."
-"If my years in the Marines taught me anything that I can pass onto you, it's that other kinds of servicemen are lazy and unprofessional."
-"As your loving father, I know what's best for you...even if you don't!"

Answer 2

Ethos is credibility. You want your audience or reader to see you as credible. Otherwise, they will dismiss what you are saying.
For example, if I were to say "Springer Spaniels are good with children," would you believe me? Probably not. Who am I? How would I know? But if I were to say "My veterinarian recommends a Springer Spaniel because they are good with children," you are more likely to believe it. A vet must know these things, right? It makes what I am saying credible to have it backed my a professional in that field.
I hope I helped.

** For the record, I have no idea if a Springer Spaniel is good with kids or not. **