sad
知道了这个坏消息后他们十分伤心.
at: 多用来表示感情上的原因,常和表示一定感情的词连用.例如：
I’m much pleased at your arrival.
你来了我非常高兴
He is angry at being delayed.
他因被耽搁而生气.
People wondered at his skill,
人们惊叹他的技艺.
常见的短语还有：be afraid at, be surprised at, be happy at, be frightened at, be sad at, be in deep sorrow at, at sight of etc.
根据文章强调是坏消息,用sad较好.