1 . 郑州市中原福塔的塔座为鼎,寓意为鼎立中原,从上空俯瞰如一朵盛开的梅花,寓意花开五福,福泽中原,它是美学与建筑的完美融合.绿地中心千玺广场“大玉米”号称中原第一高楼,璀璨繁华的外表下包含浓郁的易学设计理念,流露出馥郁的古香.这两座塔都彰显了中华文化丰富的内涵与深厚的底蕴.小米同学积极开展数学研究性学习,用以下方法测量两座塔的高度.
(1)为测量中原福塔高度,小米选择视野开阔的航海东路上一条水平基线
,使
共线,在
三点用测角仪测得
的仰角分别为
,其中测角仪的高度为
米,为了测量距离,小米骑共享单车,速度为
,从
到
耗时
,从
到
耗时为原来的
倍,求塔高
.(参考数据:取
,
)
,使
三点共线,在
两点用测角仪测得
的仰角分别为
,
,在
处测得
的仰角为
,测角仪高度忽略不计.小米使用智能手机运动测距功能,从河南艺术中心音乐厅入口台阶
处运动到水景露天剧场的
处,测得距离
.
,
,
,
表示塔高
;
②若
,
,
,
米,求千玺广场“大玉米”的实际高度.
(参考数据:取
,
,
)
(1)为测量中原福塔高度,小米选择视野开阔的航海东路上一条水平基线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2c4f20594ab1443c0d8dcce42895f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2c4f20594ab1443c0d8dcce42895f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8e3f533b62be4d6f17e949d924f03b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f9efdececbe3290745c961cf2988c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/049462dc17c95fc83c3a362f09cd0688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45035c785ad41695590eff5a9a6c0e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8020712f738b1059cefe3e64becf08b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67802092c4c9f3b1cff1f9502b7d1ded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f804d01672d4e1d904368979c3567d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.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/5b5858ee1ce52b251816757257a11c29.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/7053dbf019e52fe3791d764ba6d96b42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d58f9019097bd05037aefd5c322916.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3210a2f2bfd010609600bca988f55304.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600e64cb886417562657da9966a2fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8dc311b022e50c061cf97195f6706a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6166a4bb8ec20c446499134afb7aa3e8.png)
(参考数据:取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2bd823b33b52e016e14da84ca1f4df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac96391cc3bb0e390b1fa563f00deaeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f303268ffe2bc132e52c0fb221c9d373.png)
您最近一年使用:0次
2 . 周口市广播电视塔位于周口市区七一路和周口大道交叉口处,该塔有效地解决了周口市广播电视无线信号覆盖范围小、信号质量差的问题.发射塔由塔座、塔身、井道、塔楼和天线等
个主要部分组成(如图1所示),其中天线为传统的四边形空间桁架结构,横截面层层缩进,在外形上有着芝麻开花节节高的吉祥寓意.国庆假期,章阳同学在取得有关部门许可的前提下,利用无人机对广播电视塔进行拍照与摄像.章阳同学在地面点
处测得塔楼
的仰角为
,无人机在
处沿仰角为
的方向飞行
米后到达
处,测得
,且
,
,
,
,
五个点都在同一平面内(如图2所示).
![](https://img.xkw.com/dksih/QBM/2021/11/23/2857692062326784/2858053833318400/STEM/e903456d9f8a45e48f6930dc665e1ca6.png?resizew=554)
(1)求塔楼到地面的高度
;
(2)如果广播电视塔的天线
的长是
米,无人机从
到
的飞行过程中,在点
处观看天线
的视角为
(即
),为了拍摄到天线
最为清晰的图像,要求视角
最大.若点
处距离地面的高度
为
米,那么
为何值时,无人机拍摄到天线
的图像最清晰?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.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/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf15952853fb42e8fd9a726598f67ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3ecac7aca747ed5e6ef84d907869e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f2665526efab6fdd59a4fe1bfe4e39.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/2021/11/23/2857692062326784/2858053833318400/STEM/e903456d9f8a45e48f6930dc665e1ca6.png?resizew=554)
(1)求塔楼到地面的高度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(2)如果广播电视塔的天线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b765e032d24c1557ff29cb6f70be0a98.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/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/26689ae5eba9a29775b20d7a2dcd3ace.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/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
2021-11-24更新
|
572次组卷
|
3卷引用:专题02 解三角形(2)-【常考压轴题】
解题方法
3 . 如图,某人身高
,他站的地点
和云南大理文笔塔塔底
在同水平线上,他直立时,测得塔顶
的仰角
(点
在线段
上,忽略眼睛到头顶之间的距离,下同).他沿线段
向塔前进
到达点
,在点
直立时,测得塔顶
的仰角
:塔尖MN的视角
(
是塔尖底,在线段
上).
![](https://img.xkw.com/dksih/QBM/2021/7/1/2754872852873216/2781076809252864/STEM/98bd4bdc-fae1-4c25-b0a0-b847bfac9913.png?resizew=331)
(1)求塔高
;
(2)此人在线段
上离点
多远时,他直立看塔尖
的视角最大?说明理由.
参考数据:
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad35c8e3dc9a0a2d7e17f235593a725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21a2dfdcdab05b60a1ee81a74061e86d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4cfef623a9534b5708df5f95f1760a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d98a867c15065700a04ccf6a3b9e6529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8515118a6137f3323fa74730747559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79673bc5b6037d6516df1be25e0d2d49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4cfef623a9534b5708df5f95f1760a5.png)
![](https://img.xkw.com/dksih/QBM/2021/7/1/2754872852873216/2781076809252864/STEM/98bd4bdc-fae1-4c25-b0a0-b847bfac9913.png?resizew=331)
(1)求塔高
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4cfef623a9534b5708df5f95f1760a5.png)
(2)此人在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e21c6c8df2c8aaf99721ada68fe59cfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892c71122fab5d95df9db7a94ca62d63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39631c8b0f107dce57c8edc2ab0d8fd3.png)
您最近一年使用:0次
2021-08-07更新
|
1788次组卷
|
7卷引用:专题06正弦定理、余弦定理解的实际应用
专题06正弦定理、余弦定理解的实际应用(已下线)专题3 最佳视角 米勒定理【练】四川省达州市2020-2021学年高一下学期期末数学(理)试题(已下线)第10课时 课后 两角和、差的余弦、正弦和正切公式(2)(已下线)第13课时 课中 余弦定理、正弦定理应用举例(已下线)6.4平面向量的应用C卷(已下线)第14练 三角恒等变换-2022年【寒假分层作业】高一数学(人教A版2019选择性必修第一册)
名校
4 . 如图,
三个警亭有直道相通,已知
在
的正北方向6千米处,
在
的正东方向
千米处.
(1)警员甲从
出发,沿
行至点
处,此时
,求
的距离;
(2)警员甲从
出发沿
前往
,警员乙从
出发沿
前往
,两人同时出发,甲的速度为3千米/小时,乙的速度为6千米/小时.两人通过专用对讲机保持联系,乙到达
后原地等待,直到甲到达
时任务结束.若对讲机的有效通话距离不超过9千米,试问两人通过对讲机能保持联系的总时长?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b27567d43c5b91382ee3d7ca708ee422.png)
(1)警员甲从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efa8e51f76f13657040b91c7e117d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(2)警员甲从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://img.xkw.com/dksih/QBM/2018/6/1/1958047200518144/1962910174748672/STEM/5c36afb0d45943818b1bc930951fe751.png?resizew=205)
您最近一年使用:0次
2018-06-20更新
|
1966次组卷
|
4卷引用:专题06正弦定理、余弦定理解的实际应用
5 . 如图,有一段河流,河的一侧是以O为圆心,半径为
米的扇形区域OCD,河的另一侧是一段笔直的河岸l,岸边有一烟囱AB(不计B离河岸的距离),且OB的连线恰好与河岸l垂直,设OB与圆弧
的交点为E.经测量,扇形区域和河岸处于同一水平面,在点C,点O和点E处测得烟囱AB的仰角分别为
,
和
.
(1)求烟囱AB的高度;
(2)如果要在CE间修一条直路,求CE的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e4123975f257306440158659634c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bb3820bab977db734f4335e4fde720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/15/387d1352-f76b-4d73-b578-7e18688368ff.png?resizew=189)
(1)求烟囱AB的高度;
(2)如果要在CE间修一条直路,求CE的长.
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2016-12-03更新
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7卷引用:专题06正弦定理、余弦定理解的实际应用
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