名校
1 . 如图,位于某海域
处的甲船获悉,在其北偏东
方向
处有一艘渔船遇险后抛锚等待营救. 甲船立即将救援消息告知位于甲船北偏东
,且与甲船相距
的
处的乙船,已知遇险渔船在乙船的正东方向,那么乙船前往营救遇险渔船时需要航行的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1006d62fa5723dc36286b8f5494f993e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5841e9d2b2a8ec148fbece9c343922a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c14c6709d2a04863cacdee618b20613e.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-01-05更新
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866次组卷
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5卷引用:吉林省吉林市2024届高三上学期第二次模拟考试数学试题
吉林省吉林市2024届高三上学期第二次模拟考试数学试题(已下线)考点16 解三角形实际应用问题 --2024届高考数学考点总动员【练】(已下线)专题09 余弦定理、正弦定理的应用-《重难点题型·高分突破》(人教A版2019必修第二册)(已下线)专题11 余弦定理、正弦定理的应用-《重难点题型·高分突破》(苏教版2019必修第二册)安徽省淮南第二中学2023-2024学年高一下学期3月阶段检测数学试题
2023高三上·全国·专题练习
2 . 如图,
三地有直道相通,
千米,
千米,
千米.现甲、乙两警员同时从
地出发匀速前往
地,经过
小时,他们之间的距离为
(单位:千米),甲的路线是
,速度为
千米/小时,乙的路线是
,速度为
千米/小时,乙到达
地后在原地等待.设
时,乙到达
地;
时,乙到达
地.
与
的值;
(2)已知警员的对讲机的有效通话距离是
千米,当
时,求
的表达式,并判断
在
上的最大值是否超过
?说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2665479c5fb12e1e728716a30a219c27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df8207303326aaab6a0b763e24d857c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42a8ba3ea434605e0574339efc9c38f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4b8457e215b33fb6c4377f30bc2e75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c8ca569e742d9eeee3b85f61bd8e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6c71a0da6a878a5b12bf8a8e784645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/719a627af6b0de19823983b65637cd92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3b1e1e25b1b8633d360f0922605ff2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c7eb49a823f757461cd5260757b088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa0ed074fd35bb48b8d767adcbb0411.png)
(2)已知警员的对讲机的有效通话距离是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69f8eaa14d343655e080c9c7a49bb79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c8ca569e742d9eeee3b85f61bd8e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c8ca569e742d9eeee3b85f61bd8e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/248d9edcca636953d40ee485c487562d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
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3 . 某校高中“数学建模”实践小组欲测量某景区位于:“观光湖”内两处景点A,C之间的距离,如图,B处为码头入口,D处为码头,BD为通往码头的栈道,且
,在B处测得
,在D处测得
.(A,B,C,D均处于同一测量的水平面内)
(2)栈道BD所在直线与A,C两处景点的连线是否垂直?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10509c5515395ac694f7b3ec951d6d1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76cc881caea3de66fab1fabdc9d20da2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5321a6e65d2a431c5087f771bf6c2652.png)
(2)栈道BD所在直线与A,C两处景点的连线是否垂直?请说明理由.
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6卷引用:黑龙江省名校联盟2024届高三模拟测试数学试题
4 . 某货轮在
处看灯塔
在货轮北偏东
,距离为
nmile;在
处看灯塔
在货轮的北偏西
,距离为
nmile.货轮由
处向正北航行到
处时,再看灯塔
在南偏东
,则下列说法正确的是( )
![](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/68a4c9b697e3df2b5469b71d3b5e47a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f52f128086257ab7513889dbf6c7550.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/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6093eebca8f3ff82ce9298feb197e955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
A.![]() ![]() ![]() |
B.灯塔![]() ![]() ![]() |
C.灯塔![]() ![]() ![]() |
D.![]() ![]() ![]() |
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755次组卷
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13卷引用:黑龙江省哈尔滨市第六中学校2024年高三上学期10月月考数学试题
黑龙江省哈尔滨市第六中学校2024年高三上学期10月月考数学试题黑龙江省佳木斯市三校联考2024届高三上学期第三次调研考试数学试题(已下线)考点16 解三角形实际应用问题 --2024届高考数学考点总动员【练】6.4.3.3余弦定理、正弦定理应用举例练习(已下线)专题04 平面向量的应用 (2)-【寒假自学课】(人教A版2019)(已下线)专题13 余弦定理、正弦定理的应用-【寒假自学课】(苏教版2019)(已下线)第11章:解三角形章末检测卷-【寒假自学课】(苏教版2019)(已下线)第12讲 6.4.3 第3课时 余弦定理、正弦定理应用举例-【帮课堂】(人教A版2019必修第二册)(已下线)11.3 余弦定理、正弦定理的应用-【帮课堂】(苏教版2019必修第二册)(已下线)第6.4.3讲 余弦定理、正弦定理的应用(第3课时)-同步精讲精练宝典(已下线)第11章 解三角形 单元综合检测(重点)-《重难点题型·高分突破》(苏教版2019必修第二册)(已下线)6.4.3.3 余弦定理、正弦定理应用举例——课后作业(提升版)(已下线)6.4.3.3 余弦定理、正弦定理应用举例——课后作业(基础版)
5 . 如图所示,设A,B两点在河的两岸,要测量两点之间的距离,测量者在A的同侧,在所在的河岸边选定一点C,测出的距离是m米,
,则A,B两点间的距离为
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/ecc75175-db6c-494e-99c9-72cc82638d73.png?resizew=157)
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6 . 某林场为了及时发现火情,设立了两个观测点
和
.某日两个观测点的林场人员都观测到
处出现火情.在
处观测到火情发生在北偏西
方向,而在
处观测到火情在北偏西
方向.已知
在
的正东方向
处(如图所示),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db9e29fd9404c90e6f6e8cebd9206b81.png)
________
. (精确到
)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d36581140ebac5d28438ea63b1b23b65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](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/0f3fb33e7fb8709bd8d5db686644d50b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db9e29fd9404c90e6f6e8cebd9206b81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5fe30c67ac20cd4e8b9cc2d0d420a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a73724ad0edf3a665cb9bffb970281c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/a236a002-cf59-442a-aa8e-5fef19f14b25.png?resizew=168)
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2023高三上·全国·专题练习
7 . 如图,一架飞机从
地飞往
地,两地相距
.飞行员为了避开某一区域的雷雨云层,从机场起飞以后,就沿与原来的飞行方向成
角的方向飞行,飞行到
地,再沿与原来的飞行方向成
角的方向继续飞行
到达终点. 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/457ec07cbd57016c33cce229c434e133.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27b6d7bcb9617b7bf2155cd8c72a649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc24d605ad707ad0e76059d8a31f50d3.png)
![](https://img.xkw.com/dksih/QBM/2023/12/19/3392568140537856/3392878609727488/STEM/7321dd5cfb2b449c93479be5815b5aa2.png?resizew=244)
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8 . 已知A船在灯塔C北偏东
处,且A到C的距离为2 km,B船在灯塔C北偏西
处,A,B两船的距离为3 km,则B到C的距离为________ km.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42bbcda4a4914723f6aeb41f4bd38ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb27086a9f9d5d3979dd47e1ec84ada.png)
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9 . 如图,小刚同学从楼顶A处看楼下公园的湖边D处的俯角为
,看另一边B处的俯角为
,楼高
为
米,则楼下公园的湖宽
=____ m.(结果精确到1米,参考数据:
,
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225803a7818b0985a1b96d8e0a627251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31a14bd2a972f43d7a26a99589ad083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06fc7811f9525e8b8c833746d6af5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb1a54045c98f6963fcffed8877f1654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109f68040c0de4a3967b54615288636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac08346b8da027831bd22e2ce4d035e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02206efcf2cae6ea7368f2b0ffaf881d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/20/0ec9bf19-2c26-48bb-a2b5-006d3efa34da.png?resizew=167)
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10 . 为了测量水田两侧
两点间的距离(如图所示),某观测者在
的同侧选定一点
,测得
,则
两点间的距离为________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/e11e75c9e566cbbeba84b84c6d10989a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/63939041-a7a3-48cc-b581-bbf5c6add22e.png?resizew=163)
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