When that dog was alive, the hair on his back would often stand up when he got angry
When that dog was alive,
その犬は生きてた頃
例えば雄の犬であれば、
the hair on his back would often stand up
よく背中の毛を逆立てた
when he got angry
怒ると
the hair on his back would often bristleは通じるかもしれませんが、日常場面で聞くような表現じゃないと思います（ちょっと文学的なイメージ？）。stand upやstand on endと言う表現の方が自然でわかりやすいです。
ご参考になれば幸いです！
アメリカ合衆国 
