Question

But i can assure them that our professional advisers of the three services unitedly advise that we should carry on the war, and that there are good and reasonable hopes of final victory. which audience appeal does churchill most clearly use here?

Answer 1

The answer should be Ethos 

Answer 2

Answer: Ethos

Ethos refers to an appeal that highlights the credibility of the speaker, or whoever is making the claim. In this case, Churchill is making an appeal to ethos. He is tellings his audience that "professional advisers" believe that the war should continue, and that they have good chances of winning it. He is clearly appealing to the credibility of these experts.