Final answer:
The term to establish a trustworthy relationship with an audience is ethos, an appeal to ethics that emphasizes the speaker's or writer's credibility.
Step-by-step explanation:
The term used to describe your attempt to establish a relationship of trust with your audience and convince them you are someone they should listen to is ethos. Ethos is an appeal to ethics and is one of the three modes of persuasion identified by Aristotle, along with logos and pathos. To describe ethos effectively, it is associated with the credibility and authority of the speaker or writer, which can be established through demonstrating expertise, knowledge, and a moral character that resonates with the audience.