名校
解题方法
1 . 在
中,
所对的边分别为
,且满足
.
(1)求
;
(2)点
在线段AC的延长线上,且
,若
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f5573b30734d65648f61c0a94c98de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/340997fc3cf1c311dc550b9221858db5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32aec98e4b02f753c005ea1de0f96ce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce2efbb15151b47886b13331fe786f9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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名校
2 . 某地开展植树造林活动,拟测量某座山的高.勘探队员在山脚
测得山顶
的仰角为
,他沿着坡角为
的斜坡向上走了100米后到达
,在
处测得山顶
的仰角为
.设山高为
,若
在同一铅垂面,且在该铅垂面上
位于直线
的同侧,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e0c2455a9e796bba6861503f0fe31b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39148155ad52f0f34fccdcd3c40a99f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c978d92edf0c4c1ef8620c17df75d35e.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7日内更新
|
372次组卷
|
3卷引用:重庆市巴蜀中学校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
3 . 在
中,角
对应的边分别为
,已知
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
______ ,
的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d12de0fe32eedb8fab4fd3a50dfa7a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2bc8adc993cad5553d66285b5971f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
4 . 在
中,角
所对的边分别为
且满足
.
(1)求角
;
(2)若
为锐角三角形,且外接圆半径为1,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7132c2d8b2ff504e6c2ba36c4f6dcfaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcdf97a7098ede321f30faafa952a116.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33012983c8ebaaadc7c13978254311d4.png)
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解题方法
5 . 已知
的角
,
,
的对边分别为
,
,
,
为锐角,满足
.
(1)求
的大小;
(2)在线段
的延长线上取一点
,使得
,
且
的面积为
,求线段
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502110d39eef20341e59823e347ad656.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6402c0f9eecfcdf73f9e87ca82a6f2c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3362a45b72536c714c5107b0ae94f1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6830ebecddbd9759be626289c408e4f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ca820a456491348e72587e4fe10bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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解题方法
6 . 在
中,内角
的对边分别为
的面积为S,已知
,且
.
(1)求
;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718b5b48053888ab3b234b8cb56a0fc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de1d395e6c48c0676a1488a299479d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/904d4815a48db81e2d861783ebb135c7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c825e45000c5eb501bbcd94f29ea2433.png)
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2024-06-14更新
|
948次组卷
|
2卷引用:重庆市巴蜀中学校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
7 . 已知
的内角
的对边分别为
,若
则
边上的中线
的长为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef7fe2d8f8ff4b1cbb30e2e6b230c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8d292c421609af0cb72ca02aa6e31b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
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解题方法
8 . 炎炎夏日,上学路上若有一支冰淇淋该多么美妙啊!小明同学酷爱甜筒冰淇淋(图1),他想动手做一个甜筒模型(图2),若根据设计稿已知
为直角三角形,四边形
为直角梯形,
,
,曲线
是以
为圆心的四分之一圆弧,
,
,
,
,将平面图形
旋转一周得到小明设计的甜筒.
;
(2)小明准备将矩形
旋转所形成的几何体都用来盛装冰淇淋(如图2所示),该矩形内接于图形
,
在弧
上(不与端点
重合),点
在线段
上,
与
所在的直线重合,设
,求:
①盛装冰淇淋容器的体积
;(用
表示)
②炎热的天气下,若冰淇淋融化的时间与盛装的体积满足关系
,请计算这个冰淇淋完全融化需要的最长时间.
(3)小明想给甜筒一些新的装饰,如果修改后的甜筒俯视图如图3所示,且通过拼装后可以变成一个正四棱锥
(即俯视图可以看作一个正四棱锥
的展开图),我们记侧棱
的长为1,
,正四棱锥的表面积记作
,体积记作
.求
(将其表示为
的形式,其中
为常数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1333acc72211e3ddb9a0f8c726ce8a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f90126f831d6600522ecaa66c2a8b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f01c4faacedfe56f5127d6c0cc63cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f341b98caabf99bc683ce8407068735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4465a96d65de0f859ea4ec9e548204d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
(2)小明准备将矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec780e86f57790cf88ec761e219bf5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edaecff592cf677f45d8c54340a89f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1494be0926832f8cb95cbc7477ae685.png)
①盛装冰淇淋容器的体积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
②炎热的天气下,若冰淇淋融化的时间与盛装的体积满足关系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698295b8bd91909e0dbb581fe29a9bd0.png)
(3)小明想给甜筒一些新的装饰,如果修改后的甜筒俯视图如图3所示,且通过拼装后可以变成一个正四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/965466f8aae61f1a049e25f0325d4abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d887c94a751c97fc17d9ee6dba8590b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46dc1a9783d9539ae3b0d2049bf1a123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb84bef0f93107237d2860f477288d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715f6103c80ca9f2c1c88b1308e33704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
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解题方法
9 . 学习以下过程:若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35426df35d0b2eae48af24f5e029b8dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39fc32806172f394bbde81797aefcd82.png)
,完成下面题目:已知
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c96adab43f4e12950ff28ec902e9993.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1018d072c74bd0f5f013002751e16668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89fda0241d8ec426980f1d0d952e7eef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35426df35d0b2eae48af24f5e029b8dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39fc32806172f394bbde81797aefcd82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/113d9ba315ee03796ed4993d823bf855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd40ca9cbe17fe92d0e9f1f1c8cacf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a18cb53580e8d0e288de7ede303fc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c96adab43f4e12950ff28ec902e9993.png)
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解题方法
10 . 在
中,
分别是三个内角
的对边,若
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10b4ad6276def3b2263a4d722dae997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dbf81e07ea41022df552405b4ca1e2f.png)
A.![]() |
B.![]() |
C.若![]() ![]() ![]() |
D.![]() ![]() |
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