"Этому человеку не нравится наша музыка."
Translation:This person does not like our music.
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113
Almost. The subject is always in the nominative case. Музыка is the subject, so it's in the nominative case, and the object is человек, so it takes the dative case "человеку."
The музыка [subj.] нравится to the человеку [obj.]. The music pleases the person.
113
The sentence is structured as "Our music does not appeal to this person."
"To this person" is этому человеку. The nominative case, этот человек, declines to the dative case, этому человеку.
It wouldn't be "это" because человек is a masculine noun. Это is a neuter noun determiner
113
You're right. Literally, it translates as "this," but in English we use the word "that" in a loose sense, and in Russian the word это is used in the same loose sense. We're more likely to say "that person" than "this person," and in Russian, we're more likely to say этот человек than тот человек
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Literally, "To this person, our music doesn't please." That's how Russian "he likes" is constructed.