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191问答库 > 在锐角△ABC中，a，b，c分别为角A，B，C所对的边，且3b=2csinB．（1）求角C的大小．（2）若c=4，且△ABC

在锐角△ABC中，a，b，c分别为角A，B，C所对的边，且3b=2csinB．（1）求角C的大小．（2）若c=4，且△ABC

2025-03-15 09:11:42

推荐回答（1个）

回答1：

（1）在锐角△ABC中，a，b，c分别为角A，B，C所对的边，且
3
b=2csinB．
由正弦定理可得：
3
sinB=2sinCsinB，
∴sinC=

3

2

，角C的大小为：60°．
（2）若c=4，且△ABC的面积为4
3
，
∴

1

2

absinC＝4
3
，即ab=16，
由余弦定理可得：16=a²+b²-2abcos60°，即a²+b²=32．
∴（a+b）²=64，∴a+b=8，
∴△ABC的周长a+b+c=12．

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