题目内容
在△ABC中,
(1)若a=4,B=30°,C=105°,则b=________.
(2)若b=3,c=
,C=45°,则a=________.
(3)若AB=
,BC=
,C=30°,则∠A=________.
(1)若a=4,B=30°,C=105°,则b=________.
(2)若b=3,c=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040940748344.png)
(3)若AB=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040940748344.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040940763341.png)
(1)2
(2)无解(3)45°或135°
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040940748344.png)
(1)已知两角和一边只有一解,由∠B=30°,∠C=105°,得∠A=45°.由正弦定理,得b=
.
(2)由正弦定理得sinB=
>1,∴无解.
(3)由正弦定理
,得
,∴sinA=
.
∵BC>AB,∴A>C,∴∠A=45°或135°
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/201408240409407951279.png)
(2)由正弦定理得sinB=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040940810790.png)
(3)由正弦定理
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040940826861.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040940841939.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824040940857413.png)
∵BC>AB,∴A>C,∴∠A=45°或135°
![](http://thumb.zyjl.cn/images/loading.gif)
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