Ethos is an argument that appeals to ethics. An appeal to ethos depends on the credibility, competence and reputation of the person making the argument. A person considered as an authority on the subject she is talking about would make such an argument.
In the case of the text shown in the letter C of the question. The narrator is appealing to ethos, when he states that no information will be hidden from the nation, even if there is a delay in the delivery of the information, it will be delivered.