题目

在△ABC中，角A，B，C所对的边分别为a，b，c，满足，D是BC边上的一点． (Ⅰ) 求角B的大小； (Ⅱ) 若AC＝7，AD＝5，DC＝3，求AB的长. 答案： (Ⅰ) 由， 得，即， 根据正弦定理，，·········· 4分 所以，又， 所以．····································································································· 6分     (Ⅱ) 在△ADC中，AC＝7，AD＝5，DC＝3， 由余弦定理得， 所以ADC=120°，ADB=60°，········································································ 9分 在△ABD中，AD=5，B=45°，ADB=60°， 由正弦定理，得， 所以AB=.·············································· 12分

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