名校
解题方法
1 . 某校学生利用解三角形有关知识进行数学实践活动.
处有一栋大楼,某学生选
、
(与
在同一水平面上)两处作为测量点,测得
的距离为
,
,
,在
处测得大楼(大楼
与水平面
垂直)楼顶
的仰角
为
.
两点间的距离;
(2)求大楼的高度及二面角
的正切值.
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c56c87fd6bf8a44244ba51a9d244e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42ed2e5bd5a0f033e24008697bf4963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0ec7f8ab857cd441a82389b246230a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
(2)求大楼的高度及二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab6d47edbcc2ae6efcfd7f28e401e3e9.png)
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2 . 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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3 . 如图,甲秀楼位于贵州省贵阳市南明区甲秀路,是该市的标志性建筑之一.甲秀楼始建于明朝,后楼毁重建,改名“凤来阁”,清代甲秀楼多次重修,并恢复原名、现存建筑是宣统元年(1909年)重建.甲秀楼上下三层,白石为栏,层层收进.某研究小组将测量甲秀楼最高点离地面的高度,选取了与该楼底
在同一水平面内的两个测量基点
与
,现测得
,
,
,在
点测得甲秀楼顶端
的仰角为
,则甲秀楼的高度约为(参考数据:
,
)( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/752a105b-5da7-471d-8f85-c44018307589.png?resizew=164)
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f671608a1ec15f7748ea290fa1c8d467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39776e9158fb382a3de6eb1572bcf02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e04fdea4d0e81810489de280f05647.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/e5b73d782d5fcbf7a68baae7a2cb6a9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f108b78e815e9085da265eb2013e0a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d2082b0e4e457c2ea1e033d69d8b39d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/752a105b-5da7-471d-8f85-c44018307589.png?resizew=164)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 马尔代夫群岛是世界上风景最为优美的群岛之一,如图所示,为了测量
两座岛之间的距离,小船从初始位置
出发,已知
在
的北偏西
的方向上,
在
的北偏东
的方向上,现在船往东航行2百海里到达
处,此时测得
在
的北偏西
的方向上,船再返回到
处后,由
向西航行
百海里到达
处,测得
在
的北偏东
的方向上,则
两座岛之间的距离为_______ 百海里.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c20e88a33043f4279fff360c81006e.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/a5c6344f4cb0181eb91a1aacf203356f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/996bf3d35b6763cbc1a423b13a9df2dd.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/b10e8abf8690e4b129466ddb918bcc94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/9eb3c20687986c99537dbfc9d5b129bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
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名校
5 . 如图,为测量一座大厦AB的高度,当小明在C处时测得楼顶A的仰角为60°,接着沿BC方向行走30m至D处时测得楼顶A的仰角为30°,则大厦AB的高度是______ m.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/11/a3bc9538-0cbd-4636-9df8-cc7a8211a6b3.png?resizew=162)
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名校
6 . 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
|
866次组卷
|
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
名校
7 . 某校数学兴趣小组为了测量其高度
,在地面上共线的三点
处分别测得点
的仰角为
,且
,则高度
约为( )
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d14af8de7575341e02ee92cd0e33312b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b370bbacf54ec2f1c0b8e0ccfdd3a295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec3cd04250b6433c113451da0c0325f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dad09268b7cb8bfcbea010cb6d2a29e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/634e0ccc-15a2-4b02-ab0a-af6badbbc175.png?resizew=170)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 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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9 . 如图,某次海上联合作战演习中,红方一艘侦察艇在
处发现在北偏东
方向,相距
的水面上的
处,有蓝方一艘小艇正以每小时
的速度沿南偏东
方向前进,红方侦察艇立即以每小时
的速度,沿北偏东
方向拦截蓝方的小艇,则红方侦察艇拦截住蓝方小艇最少需要________ 小时.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918e6c74544e2cf6b41449f5249fa491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0106e58e1e237b72aea6d1878c78668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96027803078eb15ece8b4e25938c6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0fbf7b6d7ba1d762b82baaaa836f75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13837fa789ce3e561621a38c7abddeb3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/df9af04e-5c0a-4f42-bb60-6ed41fa069f3.png?resizew=159)
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2023-12-20更新
|
286次组卷
|
4卷引用:陕西省咸阳市实验中学 2022-2023学年高二上学期第三次月考数学(理)试题
陕西省咸阳市实验中学 2022-2023学年高二上学期第三次月考数学(理)试题陕西省咸阳市实验中学 2022-2023学年高二上学期第三次月考数学(文)试题(已下线)第11章 解三角形 章末题型归纳总结(2)-【帮课堂】(苏教版2019必修第二册)(已下线)专题1.8 解三角形的实际应用-重难点突破及混淆易错规避(人教A版2019必修第二册)
2023高三上·全国·专题练习
10 . 如图,小明在热气球
上看到正前方横跨河流两岸的大桥
,并测得
,
两点的俯角分别为
和
,已知大桥
的长度为
,且与地面在同一水平面上.则热气球离地面的高度为____ m.(结果保留整数,参考数据:
,
,
,
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.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/c3ad1b0a76a887783392268ae203ad22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5babe5f1ef875292b0cf9a5e97d9d934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf4b1129e02a332511dfd19aea9c985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3374625ef599a9f3d6e2b28ed127e99f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4729b86aab299eb597b4a265ba2f9a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31c63b98a75752da1e67b2466c87cff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81954e76354e09c677f4db581368f01b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/633fcf42-fae6-46f4-a450-e03c1837c3ad.png?resizew=163)
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