Question

What is/are the preposition(s) of the following sentence?: We were talking to our friend, when his dog started barking at the cat sitting next to us.

Answer 1

to, at, and to

Explanation:

Preposition precedes a noun or pronoun to express a relation to another word or element.

The words in italic are the prepositions while the word bolded are the nouns or pronoun.

to our friend
at the cat
to us

Here a the elements connected by the prepositions to the nouns and pronoun.

• talking
  to our friend

• barking
  at the cat

• sitting next
  to us

Additional:
I noticed that you put a comma between friend and when.

The clause when his dog started barking at the cat sitting next to us is called adverbial clause.

When an adverbial clause is placed at the end of the sentence, there is no need to put a comma.

But when it is placed at the beginning of the sentence, a comma is needed to separate the clause to the independent clause.

So here's how the sentence has to be written:

We were talking to our friend when his dog started barking at the cat sitting next to us.

Here's how the sentence would be written if the adverbial clause is at the beginning of the sentence:

When his dog started barking at the cat sitting next to us, we were talking to our friend.

Hope this helps.