名校
解题方法
1 .
的内角A,B,C的对边分别为a,b,c,已知
.
(1)求
的值;
(2)若
,
的面积为
,求
的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/561c8a4a7d08e1ac4a32048dfe4d4951.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6402f1010e94be78552ed4c45548b1b8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad09921d9904335a83078262ce62a473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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5卷引用:山西省忻州市2023-2024学年高一下学期5月月考数学试题
山西省忻州市2023-2024学年高一下学期5月月考数学试题河北省保定市定州市第二中学2023-2024学年高一下学期5月月考数学试题(已下线)专题05 解三角形(1)-期末考点大串讲(人教B版2019必修第四册)河北省廊坊市文安县第一中学2023-2024学年高一下学期5月月考数学试题河北省保定市定州中学2023-2024学年高一下学期5月期中考试数学试题
名校
解题方法
2 . 如图,在平面四边形ABCD中,E为线段BC的中点,
.
,求AE;
(2)若
,求AE的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b377f22aafd3742ad860f77abaacef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb12049c4ca9c62d12c884bbaa9d09.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df54bb4e7febefb181ed69139d76317d.png)
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3 . 已知
,
,
.
(1)若
,求
的值;
(2)若复数
在复平面内对应的点
满足关系式
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb18a468485cbe7848ccbf7fd9ee6e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2104fa97725f32e0c03f291a5fb8c14a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895e674e17021ffdea6dbd303aef34e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a40a402b8af0497a46bb4a2cbf24e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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4 . 如图,直四棱柱
中,底面ABCD为菱形,
,
,P,M,N分别为CD,
,
的中点.
平面
;
(2)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e0b64d25ddd18454f88e40c45d7d8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3f5dd01b683fcab010fc6ff5558c9e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183960a75956e783ee1c5dcd4776b425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96872cd6cd581ae8a861c7032e0257b4.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96872cd6cd581ae8a861c7032e0257b4.png)
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5 . 奔驰定理是一个关于三角形的几何定理,它的图形形状和奔驰轿车logo相似,因此得名.如图,P是
内的任意一点,角A,B,C所对的边分别为a,b,c,总有优美等式:
.
的内心,
,延长AP交BC于点D,求
;
(2)若P是锐角
的外心,
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6304b350f56f7ee6a0c51d9ece5ee7db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64edb981d2bd90d1dc58e9d140d3903d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/219679f2c28a0418f62d9861b7aec02f.png)
(2)若P是锐角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2264c134952d41fb9bcb90e6c72c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568c6a1484da196de32bd04994d9d3d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
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4卷引用:山西省临汾市名校联考2023-2024学年高一下学期5月质量检测数学试题
名校
6 . 在
中,角A,B,C所对的边分别为a,b,c,已知
.
(1)求角B的大小;
(2)若
,
,求
周长的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfcbf07443d54b25ab70a0f2d4093c75.png)
(1)求角B的大小;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b2139fd92090785e08fbdf814c41f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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4卷引用:山西省临汾市名校联考2023-2024学年高一下学期5月质量检测数学试题
山西省临汾市名校联考2023-2024学年高一下学期5月质量检测数学试题金科新未来大联考2023-2024学年高一下学期5月质量检测数学试题河南省南阳市第一中学校2023-2024学年高一下学期5月月考数学试题(已下线)专题05 解三角形大题常考题型归类-期期末考点大串讲(人教B版2019必修第四册)
名校
解题方法
7 . 在
中,内角A,B,C所对的边分别为a,b,c,且
.
(1)求A;
(2)已知
,D是边BC的中点,且
,求AD的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee414de6910f495ae15e03b1a75d6e9.png)
(1)求A;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21143d45f8a1eec5a18f3b82c78ac217.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
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解题方法
8 . 已知向量
,
满足
,
,
.
(1)求
在
上的投影向量;
(2)若向量
与
垂直,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13fc7a342293983cc4865498c121493d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a31604d8909d500e9047e9a3b1f5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c8afe4cf057c5b05216efe199b6780.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa53e6f54e190da611f9f18ee20076d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0f5d6389672e98b7a226d86706c390.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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9 . 已知向量
,
,函数
.
(1)求函数
的解析式和图象的对称中心;
(2)若函数
的图象向左平移
个单位长度,得到函数
的图象,且关于x的方程
在
上有3个不同的解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75a32e46a885a0e63daa9e6a9af718ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da2030c925bd33a207324870d575c6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1659f0a03b6c37d87a0ff5e112ee3d2b.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aeb076bad84890e24dbdc945ad543cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6d922c3e98888718eadbf5e253648f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c23b25b89fc6cfa5e5497ad8c0be76ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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解题方法
10 . 如图,在正三棱台
中,
,
,
,
分别是
,
的中点,
为
上一点.
是
的中点,求证:
平面
;
(2)若
平面
,求点
的位置,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d62cf21dc5eb909126a9c2eceae0ee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cafffabb4d08d4977638e4cd9bd0356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb841d975d5c7ab05598040e99df6825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b7903de4be7d5dc1175cfbf6e8da9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1c920d02068d0e63ffdab70786c526d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34bccafd3d4688f1bc1cfbeaf7a2993a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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