名校
解题方法
1 . 某科学考察队在某地考察时,在距离
点20千米处的西侧、东侧分别设立了站点
、
.现以
为坐标系原点,
的东侧为
轴正方向,
的北侧为
轴正方向建立平面直角坐标系.
(1)若考察发现一点
满足
(千米),据此写出
所在的曲线方程;若进一步观察到,
在
的北偏东
方向处,求
点的坐标;
(2)若考察发现一点
满足
(千米).为进一步得到
位置,该考察队在距离
点15千米处的南侧、北侧分别设立了站点
、
,且
(千米),求
的距离(精确到1米)和点
相对于
的方向(精确到
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)若考察发现一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63706d833c1b4b4173f5bb53feb31c84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若考察发现一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d5ad149905e01e6d7fe38216936c21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57de927f4e5a824584d43ab8fb9ff6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a840804ee07144f46c9c2a33e33ae450.png)
您最近一年使用:0次
名校
2 . 如图所示,我国黄海某处的一个圆形海域上有四个小岛,小岛
与小岛
、小岛
相距都为5公里,与小岛
相距为
公里.已知角
为钝角,且
.
与小岛
之间的距离;
(2)记
为
,
为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d52429c8324350309f77e7209a5c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ee608882881caff2f1e223177424ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9d16fab0f52c8af5abba0bf19a06ea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76bc8e50eeccced1d7f3bc52e09a7d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d8d24b6d6dd0717c226569e345d9f0.png)
您最近一年使用:0次
2022-12-28更新
|
926次组卷
|
7卷引用:上海市曹杨第二中学2021-2022学年高一下学期期中数学试题
上海市曹杨第二中学2021-2022学年高一下学期期中数学试题(已下线)第12讲 余弦定理、正弦定理的应用(已下线)6.4.3.3 余弦定理、正弦定理在几何和生活应用举例1-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)(已下线)6.4.3第3课时余弦定理、正弦定理应用举例(精讲)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)上海市行知中学2022-2023学年高一下学期期中数学试题广东省珠海市2022-2023学年高一下学期期中数学试题广东省深圳市南头中学2023-2024学年高一下学期期中考试数学试卷
3 . 如图所示,某人为“花博会”设计一个平行四边形园地,其顶点分别为
(
),
米,
,
为对角线
和
的交点.他以
、
为圆心分别画圆弧,一段弧与
相交于
、另一段弧与
相交于
,这两段弧恰与
均相交于
.设
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/08547fc4-2573-46fa-acae-6c3297a4ccb3.png?resizew=264)
(1)若两段圆弧组成“甬路”
(宽度忽略不计),求
的长(结果精确到
米);
(2)记此园地两个扇形面积之和为
,其余区域的面积为
.对于条件(1)中的
,当
时,则称其设计“用心”,问此人的设计是否“用心”?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6032aee742b136f8ea08073426fcb2d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b977b90953db923c95e4a1643202b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3afdb528817a379a5f67f39fc32741ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fa7a2d83e2d14f51579ba94a96a4f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4841a7238ffb7413e715d0dfde3c15f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473913c0887bb64d386f4c02f1853452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fb5c6efc2550a7b39a43708d8b8b1b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fa7a2d83e2d14f51579ba94a96a4f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963dc96d575fec548fa582c4a38f5298.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/08547fc4-2573-46fa-acae-6c3297a4ccb3.png?resizew=264)
(1)若两段圆弧组成“甬路”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(2)记此园地两个扇形面积之和为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8161dc93e1752d1b565ada8729176399.png)
您最近一年使用:0次
名校
解题方法
4 . 某居民小区为缓解业主停车难的问题,拟对小区内一块扇形空地
进行改建.如图所示,平行四边形
区域为停车场,其余部分建成绿地,点
在围墙
弧上,点
和点
分别在道路
和道路
上,且
米,
,设
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/087a7d09-cf5d-4d41-a0db-4b986044ed0b.png?resizew=149)
(1)求停车场面积
关于
的函数关系式,并指出
的取值范围;
(2)当
为何值时,停车场面积
最大,并求出最大值(精确到
平方米).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c40b8789cc8d81b3cf64f0b318ab982a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef6138f7648bb46524b4ab42e661fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a99c751c30b3784cd27036b4a5b48b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259728433d68902065408fb6a34c6d4d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/087a7d09-cf5d-4d41-a0db-4b986044ed0b.png?resizew=149)
(1)求停车场面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87796ee30e6c5d5e6b6285b32abe10c.png)
您最近一年使用:0次
2020-02-29更新
|
1040次组卷
|
6卷引用:2020届上海市普陀区高考一模数学试题
名校
5 . 如图,A、B、C、D都在同一个与水平面垂直的平面内,B、D为两岛上的两座灯塔的塔顶,测量船于水面A处测得B和D点的仰角分别为75°、30°,于水面C处测得B点和D点的仰角均为60°,AC=1千米.
(2)计算B、D之间的距离(结果精确到米)
(2)计算B、D之间的距离(结果精确到米)
您最近一年使用:0次
6 . 在位于城市A南偏西
相距100海里的B处,一股台风沿着正东方向袭来,风速为120海里/小时,台风影响的半径为
海里
(1)若
,求台风影响城市A持续的时间(精确到1分钟)?
(2)若台风影响城市A持续的时间不超过1小时,求
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/260200d547998bcac50a4a491382e7f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc737fd634e2649874ab18563301beb.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212240ee594d2bd72af855928cdab0be.png)
(2)若台风影响城市A持续的时间不超过1小时,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
您最近一年使用:0次
2020-02-04更新
|
124次组卷
|
2卷引用:2016届上海市普陀区高三三模(文科)数学试题
13-14高三下·北京海淀·期末
名校
7 . 如图所示,为了测量某湖泊两侧
间的距离,李宁同学首先选定了与
不共线的一点
,然后给出了三种测量方案:(
的角
所对的边分别记为
):
① 测量
② 测量
③测量![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe588827cab14841a3e206401b814a8.png)
则一定能确定
间距离的所有方案的序号为
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/afd2738f-8fab-43c0-8e56-8d6b0465b2c5.png?resizew=105)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
① 测量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dddeafbff14ae6125ac7b9e0093194b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a670e260518d5224e588db3e293e868.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe588827cab14841a3e206401b814a8.png)
则一定能确定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/afd2738f-8fab-43c0-8e56-8d6b0465b2c5.png?resizew=105)
A.①② | B.②③ | C.①③ | D.①②③ |
您最近一年使用:0次
2016-12-03更新
|
1346次组卷
|
9卷引用:上海市普陀区曹杨二中2017-2018学年高一下学期期中数学试题
上海市普陀区曹杨二中2017-2018学年高一下学期期中数学试题(已下线)2014届北京市海淀区高三下学期期末练习(二模)文科数学试卷上海市虹口区2016届高三上学期12月模拟数学试题(已下线)测试卷36 解三角形(B)-2021届高考数学一轮复习(文理通用)单元过关测试卷沪教版(2020) 必修第二册 同步跟踪练习 第6章 三角 6.3.3 解三角形的应用沪教版(2020) 必修第二册 同步跟踪练习 第6章 6.3.2余弦定理沪教版(2020) 一轮复习 堂堂清 第三单元 3.5 正弦定理,余弦定理(一)6.1第3课时 用余弦定理正弦定理解三角形 课后习题2020-2021学年高一数学北师大版(2019)必修第二册第二章 6.1第3课时 用余弦定理、正弦定理解三角形-北师大版(2019)高中数学必修第二册