1 . 如图,为测量武汉防汛纪念碑
的高度及取景点
与
之间的距离(
在同一水平面上,雕像垂直该水平面于点
,且
三点共线),华中师大一附中研究性学习小组同学在
三点处测得顶点
的仰角分别为
,若
米,则纪念碑的高度为______ 米,取景点
与
之间的距离为______ 米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
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2 . 某货轮在
处看灯塔
在货轮北偏东
方向上,距离为
n mile;在
处看灯塔
在货轮的北偏西
方向上,距离
.货轮由
处向正北航行到
处时,再看灯塔
在南偏东
方向上,
处与
处之间的距离是__________ n mile,灯塔
与
处之间的距离是 __________ n mile.
![](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/55c12aeebfa1af16f325c98a43bb08c1.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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名校
3 . 如图,用无人机测量一座小山的海拔与该山最高处的古塔
的塔高,无人机的航线与塔
在同一铅直平面内,无人机飞行的海拔高度为
,在
处测得塔底
(即小山的最高处)的俯角为
,塔顶
的俯角为
,向山顶方向沿水平线
飞行
到达
处时,测得塔底
的俯角为
,则该座小山的海拔为_______
;古塔
的塔高为_______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3fedeef066be493469797b2ccae39f.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/79a97bb4dcfab4ec7539bc783d563c49.png)
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2024-03-26更新
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652次组卷
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11卷引用:山西省大同市第二中学校2023-2024学年高一下学期3月月考数学试题
山西省大同市第二中学校2023-2024学年高一下学期3月月考数学试题河南省洛阳市洛阳强基联盟2023-2024学年高一下学期3月联考数学试题山西省太原师范学院附属中学2023-2024学年高一下学期3月质量检测数学试题(已下线)高一 模块3 专题1 第2套 小题进阶提升练(已下线)模块五 专题5 全真拔高模拟1(高一人教B版期中)(已下线)高一 模块3 专题1 第2套 小题进阶提升练1(已下线)模块五 专题5 全真拔高模拟1(北师版高一期中)河北省沧州市运东四校2023-2024学年高一下学期4月期中考试数学试题(已下线)模块五 专题5 全真拔高模拟1(苏教版期中研习高一)(已下线)9.2 正弦定理与余弦定理的应用-【帮课堂】(人教B版2019必修第四册)(已下线)高一下学期期中考试(三角函数、向量、解三角形、复数)-学重难点突破及混淆易错规避(人教A版2019必修第二册)
4 . 海岛上有一座高塔,高塔顶端是观察台,观察台海拔
.在观察台上观察到有一轮船该轮船航行的速度和方向保持不变.上午11时,测得该轮船在海岛北偏东
,俯角为
处,11时20分测得该轮船在海岛北偏西
,俯角为
处,则该轮船的速度为______ m/h,再经过______ 分钟后,该轮船到达海岛的正西方向.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22c5729584c8dce7264e11704c61e199.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
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5 . 在一次海上联合作战演习中,红方一艘侦察艇发现在北偏东
方向,相距12公里的水面上,有蓝方一艘小艇正以每小时10公里的速度沿南偏东
方向前进,若侦察艇以每小时14公里的速度,沿北偏东
方向拦截蓝方的小艇.若要在最短的时间内拦截住,则红方侦察艇所需的时间为__________ 小时,角
的正弦值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a4c9b697e3df2b5469b71d3b5e47a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c4294a63ea631f110d517305e74e27.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/1/ac25fd00-53c4-4d25-a328-ea1280807a1a.png?resizew=151)
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2023-10-12更新
|
547次组卷
|
9卷引用:广东省六校(广州市第二中学等)2024届高三上学期第二次联考数学试题
广东省六校(广州市第二中学等)2024届高三上学期第二次联考数学试题(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【讲】(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)6.4.3余弦定理、正弦定理(第4课时)(已下线)专题11.3余弦定理、正弦定理的应用-重难点突破及混淆易错规避(苏教版2019必修第二册)(已下线)高一 模块3 专题1 第2套 小题入门夯实练内蒙古自治区通辽市第一中学2023-2024学年高一下学期第一次月考(4月)数学试题(已下线)高一 模块3 专题1 第2套 小题入门夯实练(苏教版)(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)
6 . 魏晋时期的刘徽在其所撰《海岛算经》中,运用二次测望法解决实际测量问题,是世界测量学上取得的伟大成就.某数学学习小组受《海岛算经》中“望山松”一题的启发,进行了如下测量实践活动:如图,为测量山顶松树的高
,在山底
所在水平面内,选择
、
两点,使
、
、
三点在同一直线上,在
点测得
点和
点的仰角分别为60°、45°,在
点测得
点的仰角为30°,测得基线
的长为100米.由以上测量数据可得出:①松树的高![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
______ 米(精确到0.1);②
和
分别是人在
点和
点观测松树的视角,其大小关系为:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/868ff1350bd72625328c85c3097cd85e.png)
______
(填“>”,“<”或“=”).(参考数据:
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/17/9ce1698a-e5ac-454f-af53-aa3749b90a6f.png?resizew=229)
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7 . 武当山,位于湖北省西北部十堰市境内,其自然风光以雄为主,兼有险、奇、幽、秀等多重特色.主峰天柱峰犹如金铸玉琢的宝柱雄峙苍穹,屹立于群峰之巅.环绕其周围的群山,从四面八方向主峰倾斜,形成独特的“七十二峰朝大顶,二十四涧水长流”的天然奇观,被誉为“亘古无双胜境,天下第一仙山”.如图,若点
为主峰天柱峰的最高点,
为观测点,且
在同一水平面上的投影分别为
,满足
,在点
处测得点
的仰角为
,
米,在点
处测得点
的仰角为
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a71a9d21f77e9535de152bb33f802bb.png)
__________ 米,
两点到水平面
的高度差为__________ 米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/20/5a74a5f3-a742-4856-ac43-d9876666f9e6.png?resizew=319)
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8 . 如图,为了测量山高BC,分别选择山下平地的A处和另一座山的山顶M处为测量观测点.从A点测得M点的仰角
,C点的仰角
以及
,从M点测得
,已知山高
米,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2952b68243e0fd29a7178208e3d46da8.png)
________ ,山高![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca90e8a784f990c4097eec9219908d.png)
________ 米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42ac94c7c00b01d34a39e72cc4ee517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab926d89b65f26c12e3da73ef1e5cf68.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca90e8a784f990c4097eec9219908d.png)
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2023-06-16更新
|
254次组卷
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2卷引用:重庆市渝东九校联盟2022-2023学年高一下学期期中数学试题
9 . 如图,为测塔高,在塔底所在的水平面内取一点C,测得塔顶的仰角为θ,由C向塔前进30米后到点D,测得塔顶的仰角为2θ,再由D向塔前进米后到点E,测得塔顶的仰角为4θ,则θ=
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10 . 如图,在海岸
处,发现北偏东
方向,距离
为
的
处有一艘走私船,在
处北偏西
方向,距离
为
的
处有一艘缉私艇奉命以
的速度追截走私船,此时,走私船正以
的速度从
处向北偏东
方向逃窜.则缉私艇沿北偏东________ 方向行驶才能最快追上走私船,需要的时间是________
.
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您最近一年使用:0次
2023-08-01更新
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230次组卷
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2卷引用:湖北省武汉市江岸区2020-2021学年高一下学期期末数学试题