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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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)
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![](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/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c809a5f119388d56404c0175dfd6c295.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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3 . 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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4 . 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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5 . 某人从山的一侧
点看山顶的仰角为
,然后沿从
到山顶的直线小道行走
到达山顶,然后从山顶沿下山的直线小道行走
到达另一侧的山脚
处
在同一水平面内,山顶宽度忽略不计),则其从
点看山顶的仰角的正弦值为__________ ,
的最大值为__________
.
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1af91614bf00ce2a661d2460c7afd335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05ba29eb90358e2211e1f7ba6423fa2.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
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6 . 一艘客船在
处测得灯塔
在它的北偏东
,在
处测得灯塔
在它的北偏西
,距离为
n mile.客船由
处向正北航行
n mile到达
处,再看灯塔
在它的南偏东
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
______ n mile;设灯塔
在
处的南偏西
度,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b657cfa91b6394e4b00fa385a2c0149.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b657cfa91b6394e4b00fa385a2c0149.png)
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7 . 在一次抗洪抢险中,某救生艇发动机突然发生故障停止转动,失去动力的救生艇在洪水中漂行.此时,风向是北偏东
方向,风速是
;水的流向是正东方向,流速是
.若不考虑其他因素,救生艇在洪水中漂行的速度的方向为北偏东_____________ 方向,大小为___________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35ec490c4c13a411dd5fd0689d12b931.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35ec490c4c13a411dd5fd0689d12b931.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ca55c030e7d88040525c4fb9a278f8.png)
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8 . 如图所示,A,B,C为三个村庄,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41db498f025052df2dbb1e50ab672675.png)
___________ ;若村庄D在线段BC中点处,要在线段AC上选取一点E建一个加油站,使得该加油站到村庄A,B,C,D的距离之和最小,则该最小值为___________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc78b1cd26ab7a3b4b2819515fbe7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a12f98eabd59eb2f973624f9d97466c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52a9baa1e6ec310c1d02cbc57ce631a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41db498f025052df2dbb1e50ab672675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5fe30c67ac20cd4e8b9cc2d0d420a7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/1/89614a18-03d7-4b48-b1ae-48fbc822bba9.png?resizew=185)
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9 . 如图,B是线段
上一点,点D位于点A的北偏东
方向上,位于点B的正北方向上,位于点C的北偏西
方向上,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c978d92edf0c4c1ef8620c17df75d35e.png)
___________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ec5d678ec42846e1d28301e3bfd4be.png)
___________ ;(答案精确到小数点后两位)(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a4c9b697e3df2b5469b71d3b5e47a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24325de3e429dbfdd9df7a2cdd8b3b1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c978d92edf0c4c1ef8620c17df75d35e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ec5d678ec42846e1d28301e3bfd4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13bbe09991c8103bb908e5bd7cc1a9db.png)
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2022-07-05更新
|
312次组卷
|
2卷引用:江西省萍乡市2021-2022学年高一下学期期末考试数学试题
10 . 如图,位于我国南海海域的某直径为
海里的圆形海域上有四个小岛,已知小岛B与小岛C相距为5海里(小岛的大小忽略不计,测量误差忽略不计),经过测量得到数据:
.则小岛B与小岛D之间的距离为___________ 海里;小岛C与小岛D之间的距离为___________ 海里.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b947152b672cf56e5a8cde6800d71c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfdc4dbfdd0c480ffdf57729163c1abb.png)
![](https://img.xkw.com/dksih/QBM/2022/4/29/2968519797211136/2969261709197312/STEM/fbdc31d6-6891-4e4a-b70c-8e6b03c6cefc.png?resizew=180)
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2022-04-30更新
|
201次组卷
|
2卷引用:江苏省苏州市吴县中学2021-2022学年高一下学期期中数学试题