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！
When our dog was still alive and he got angry, the hair on his back bristled.
この場合、次のような言い方ができますよ。
ーWhen our dog was still alive and he got angry, the hair on his back bristled.
「うちの犬がまだ生きていた時、彼は怒ると背中の毛を逆立てた」
to bristle「毛を逆立てる」
ご参考まで！
アメリカ合衆国 
カナダ 
