Question

如图5，中，点在线段上，且，

（Ⅰ）求的长；

（Ⅱ）求的面积．

 

图5

 

Answer 1

解：（Ⅰ）因为，所以.······················ 2分

在中，设，

则由余弦定理可得  ①························································ 5分

 在和中，由余弦定理可得，

．··········································································· 7分

因为，

所以有，所以3＝－6   ②

由①②可得，即．································································ 9分

（Ⅱ）由（Ⅰ）得的面积为，

所以的面积为．········································································· 12分

（注：也可以设，所以，用向量法解决；或者以为

原点，为轴建立平面直角坐标系，用坐标法解答；或者过作平行线交延长线于，用正余弦定理解答．具体过程略）