1 . 如图,某渔船在海上
处捕鱼时,天气预报几小时后会有恶劣天气,该渔船的东偏北
方向上有一个小岛
可躲避恶劣天气,在小岛
的正北方向有一航标灯
距离小岛25海里,渔船向小岛行驶50海里后到达
处,测得
,
海里.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/9eadffcb-089f-4ac1-8ce5-d95a08c88a6d.png?resizew=161)
(1)求
处距离航标灯
的距离
;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/c5db41a1f31d6baee7c69990811edb9f.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/f9d74d47d93f5540e801834aa71b3bc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac3e4d0628673acaef12954a56a01ca.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/9eadffcb-089f-4ac1-8ce5-d95a08c88a6d.png?resizew=161)
(1)求
![](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/03902478df1a55bc99703210bccab910.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
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808次组卷
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8卷引用:上海市南汇中学2022-2023学年高一下学期期中数学试题
上海市南汇中学2022-2023学年高一下学期期中数学试题黑龙江省齐齐哈尔市恒昌中学校2022-2023学年高一下学期期中数学试题(已下线)第6章 三角-同步精品课堂(沪教版2020必修第二册)安徽省合肥艺术中学2020-2021学年高一下学期第一次调研考试数学试题(已下线)第13课时 课中 余弦定理、正弦定理应用举例山东省枣庄市滕州市第一中学2021-2022学年高一下学期3月月考数学试题山东省枣庄市市中区第三中学2021-2022学年高一下学期3月月考数学试题黑龙江省哈尔滨市第十一中学校2022-2023学年高一下学期4月月考数学试题
2 . 如图,测量河对岸的塔高AB时,可以选与塔底B在同一水平面内的两个测点C与D,测得∠BCD
,
,
米,并在点C测得塔顶A的仰角为
,则塔高AB为___________ 米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd81657e13368e335720ab0baf861d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c49a35146eec0090b1269283829984bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2aea5dc133fdded83d5453ee447deff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://img.xkw.com/dksih/QBM/2021/5/13/2720395434917888/2800990358544384/STEM/8b909dd2c55a46c8910c1c4fe1925657.png?resizew=242)
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3 . 已知地球的半径约为6371千米.上海的位置约为东经121°、北纬31°,大连的位置约为东经121°、北纬39°,里斯本的位置约为西经
、北纬39°.则大连与里斯本之间的球面距离为______ (结果精确到千米).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3f9c270c34c12a3253fcb14a70255cf.png)
![](https://img.xkw.com/dksih/QBM/2021/5/5/2714540797952000/2800146813411328/STEM/e7e17138-9cc2-46bd-ba84-3525e037b036.png?resizew=269)
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名校
解题方法
4 . 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
公里,与小岛
相距公里
(其中
为常数),已知角
为钝角,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/4f572de0-f84b-40d4-af22-e6ca10e78f12.png?resizew=162)
(1)求小岛
与小岛
之间的距离;(用
表示)
(2)求四个小岛所形成的四边形
的面积;(用
表示)
(3)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/a3f3383decde66462a311444366c4bce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7bf4594e1e656c8afaaf008504509d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ee608882881caff2f1e223177424ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/4f572de0-f84b-40d4-af22-e6ca10e78f12.png?resizew=162)
(1)求小岛
![](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/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)求四个小岛所形成的四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)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)
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2021-08-26更新
|
468次组卷
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3卷引用:上海市建平中学2020-2021学年高一下学期期中数学试题
5 . 一船向正北方向匀速航行,看见正西方向有相距
海里的两个灯塔恰好与它在一条直线上,船继续航行一小时后,看见一灯塔在船的南偏西
方向,另一灯塔在船的南偏西
方向,则这艘船的航行速度是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c12aeebfa1af16f325c98a43bb08c1.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10卷引用:期中全真模拟试卷(4)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)
(已下线)期中全真模拟试卷(4)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)湖北省孝感市普通高中协作体2020-2021学年高一下学期期中数学试题山东省泰安市第三中学2022-2023学年高一下学期期中考试数学试题(已下线)6.4.3+第3课时+余弦定理、正弦定理的应用举例(分层练习)-2020-2021学年高一数学新教材配套练习(人教A版2019必修第二册)福建省福州市平潭县新世纪学校2020-2021学年高一下学期月考(一)数学试题湖北省宜昌市夷陵中学2020-2021学年高一下学期3月质量检测数学试题广西平果第三高级中学2020-2021学年高一下学期第一次月考数学试题江西省赣县第三中学2020-2021学年高一5月月考数学(理)试题河北省石家庄市二十七中2020-2021学年高一下学期第一次月考数学试题广东省广州市番禺区洛溪新城中学2020-2021学年高一下学期4月月考数学试题
6 . 如图所示,甲船在距离
港口
海里,并在南偏西
方向的
处驻留等候进港,乙船在
港口南偏东
方向的
处沿直线行驶入港,甲、乙两船距离为
海里.当乙船行驶
海里到达
处,接到港口指令,前往救援忽然发生火灾的甲船,此时甲、乙两船之间的距离为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e60fbe6820130fb20abc555a94b5ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5328421f88e455d62909e5166122633.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/2bb27086a9f9d5d3979dd47e1ec84ada.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34584b79ec2246f47aeed8855d2762c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7f27ebcef70a3ebbbe8d2e53ea0896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/7ceee454-8f89-4a33-b97b-9c3c4ff123eb.png?resizew=144)
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名校
7 . “伦敦眼”坐落在英国伦敦泰晤士河畔,是世界上首座观景摩天轮,又称“千禧之轮”,该摩天轮的半径为6(单位:
),游客在乘坐舱
升到上半空鸟瞰伦敦建筑
,伦敦眼与建筑之间的距离
为12(单位:
),游客在乘坐舱
看建筑
的视角为
.
在伦敦眼的最高点
时,视角
,则建筑
的高度为_____ (单位:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167e6e41ac221847824a72e964f340f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167e6e41ac221847824a72e964f340f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d7b9d9bf0d5fc25c99170ab27fa4045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167e6e41ac221847824a72e964f340f1.png)
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3卷引用:上海市上海外国语大学附属浦东外国语学校2020-2021学年高一下学期期中数学试题
上海市上海外国语大学附属浦东外国语学校2020-2021学年高一下学期期中数学试题山东省嘉祥县第一中学2020-2021学年高一下学期6月份月考数学试题(已下线)必考考点3 解三角形与实际应用 专题讲解 (期末考试必考的10大核心考点)
8 . 如图,折线
为海岸线,
km,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/bda86beb-0c42-4a02-8d94-b900036393cc.png?resizew=129)
(1)求
的长度;
(2)若
km,求D到海岸线
的最短距离. (以上答案都精确到0.001km)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0cc6293cfedec30b124ece908c4c438.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33fb0b06f176e59dbe20f17a94a68c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0c8008edad41d576b44024532c83a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd893bb2f4c04219678d9cea126a240d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae916162e4654626a8f8090e856f5af.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/bda86beb-0c42-4a02-8d94-b900036393cc.png?resizew=129)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd4997da49b3dfe98144ad13aed0d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0cc6293cfedec30b124ece908c4c438.png)
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2021-12-12更新
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331次组卷
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2卷引用:上海市位育中学2019-2020学年高一下学期期中数学试题
9 . 甲船在距离
港口
海里并在南偏西
方向的
处驻留等候进港,乙船在
港口南偏东
方向的
处沿直线行驶入港,甲、乙两船距离为
海里.乙船的速度为每小时
海里,经过
分钟航行到
处,求此时甲、乙两船相距多少海里?甲在乙的什么方向?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da45c443af7994a26ffa9d8894e7262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3f9c270c34c12a3253fcb14a70255cf.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/a5328421f88e455d62909e5166122633.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c423cfa71956862edbed10a5ba12d0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b837fd9c52f60bfb3b6852733abc790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b7f27ebcef70a3ebbbe8d2e53ea0896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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2021-07-25更新
|
340次组卷
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3卷引用:上海市奉贤中学2020-2021学年高一下学期期中数学试题
名校
10 . 如图,某大型厂区有三个值班室
、
、
.值班室
在值班室
的正北方向
千米处,值班室
在值班室
的正东方向
千米处.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/77acea28-7724-4576-96bb-23a5b281cfa9.png?resizew=188)
(1)保安甲沿
从值班室
出发行至点
处,此时
,求
的距离;
(2)保安甲沿
从值班室
出发前往值班室
,保安乙沿
从值班室
出发前往值班室
,甲乙同时出发,甲的速度为
千米/小时,乙的速度为
千米/小时,若甲乙两人通过对讲机联系,对讲机在厂区内的最大通话距离为
千米(含
千米),试问有多长时间两人不能通话?
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.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/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/77acea28-7724-4576-96bb-23a5b281cfa9.png?resizew=188)
(1)保安甲沿
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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