1 . 某地需要经过一座山两侧的
两点修建一条穿山隧道.工程人员先选取直线
上的三点
,在隧道
正上方的山顶
处测得
处的俯角为
,
处的俯角为
,
处的俯角为
,且测得
,
,
,则拟修建的隧道
的长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c12e76fbd84eeec721386bd3b04cc4.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8686e04d2e83eeec0f278419caa535c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/371ed1dc33ec2969f20cb0ff1d652237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe34607b65d5071186acd395f176eab4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
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解题方法
2 . 在
中,内角
,
,
所对的边分别为
,
,
,已知
, ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1bbcbde20ddc88849c2941b7f52735.png)
(1)求角
;
(2)求
的外接圆面积;
(3)若
为
的内心,求
周长的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f002f960ec07ea229ed243e2d991d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1bbcbde20ddc88849c2941b7f52735.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
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3 . 10世纪波斯著名数学家、天文学家阿尔·库希设计出一种方案,通过两个观测者异地同时观察同一颗流星,来测定其发射点的高度,如图,假设地球是一个标准的球体,
为地球的球心,弧
为地线,有两个观测者在地球上的
两地同时观测到一颗流星
,观测的仰角分别为
,其中
,为了方便计算,我们考虑一种理想状态,假设两个观测者在地球上的
两点测得
,地球半径为
千米,两个观测者的距离弧
千米.(参考数据:
)
发射点的近似高度
.
(2)在古希腊时代,科学不发达,人们看到流星以为这是地球水分蒸发后凝结的固体.已知对流层(地球大气层靠近地面的一层)高度大约在18千米左右,若地球半径
千米,请你据此判断该流星
是地球蒸发物还是“天外来客”,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2447971258541c8fa18372e2f062b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cdd6cfa7ac434726640df73e0e8066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83e7ad1c0478dc9fb88679c4c385e54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c0adcf16f0d702752c05aeeee874b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe864bd478c5acacc0e3d9d206cadbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debb80b9affaee81c10743a47437667f.png)
(2)在古希腊时代,科学不发达,人们看到流星以为这是地球水分蒸发后凝结的固体.已知对流层(地球大气层靠近地面的一层)高度大约在18千米左右,若地球半径
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa51fc110ae4f8fc059bc84bc0fc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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4 . 郑州二七塔是为了纪念二七大罢工而修建,是中国建筑独特的仿古联体双塔,小米同学为了测量二七塔的塔高
,在塔底所在的水平面内取点
,测得塔顶的仰角为
,前进
米后到达
点,测得塔顶的仰角为
,再前进
米后到达
点,测得塔顶的仰角为
,则塔高![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3832567a1c20860ea4d648243085acd.png)
_________ 米.(参考数据:
,最终结果保留整数,即结果精确到
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d58f9019097bd05037aefd5c322916.png)
![](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/110e329d74716ab387dc602bb2b4f998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267572d2dff2dc38cf9251b7f33a3e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c1d6748b75b0e1fbaddc705a230a1a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883f0416477ddaa8b2a68a8d88063a62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3832567a1c20860ea4d648243085acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae69c01eff3ccfdd0853d9854b7777de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f328ba89c0a92a4447788b65571f7aa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/49e1da89-45e0-4b26-8e87-d7c3ce326bee.png?resizew=216)
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5 . 某日,中国海军护航编队太原舰在A处收到某商船在航行中发出的求救信号后,立即测出该商船在方位角(是从某点的指北方向线起,依顺时针方向到目标方向线之间的水平夹角)为
、距离A处为
的C处,并测得该商船正沿方位角为
的方向,以
的速度航行,太原舰立即以
的速度前去营救.
(1)太原舰最少需要多少小时才能靠近商船?
(2)在营救时间最少的前提下,太原舰航行的方位角约是多少?
(角度精确到
,参考数据:
,
,
.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf333d56bd13646b105ef876b432f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b975f35ecfc9641688e682bcee70e1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8840a3d48151a6ca789ffda84897cd60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9532132b349ceeca724a2a3d8ba2e623.png)
(1)太原舰最少需要多少小时才能靠近商船?
(2)在营救时间最少的前提下,太原舰航行的方位角约是多少?
(角度精确到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c74a88e12936aaa3518764d5fb5192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb160075701398eeeee687162323f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95042fa5ccc55462334c77fdab835e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47bb3f35e3db7c1f3a3dd3eb20151b5f.png)
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解题方法
6 . 某校高中“数学建模”实践小组欲测量某景区位于:“观光湖”内两处景点A,C之间的距离,如图,B处为码头入口,D处为码头,BD为通往码头的栈道,且
,在B处测得
,在D处测得
.(A,B,C,D均处于同一测量的水平面内)
(2)栈道BD所在直线与A,C两处景点的连线是否垂直?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10509c5515395ac694f7b3ec951d6d1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76cc881caea3de66fab1fabdc9d20da2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5321a6e65d2a431c5087f771bf6c2652.png)
(2)栈道BD所在直线与A,C两处景点的连线是否垂直?请说明理由.
您最近一年使用:0次
2024-04-05更新
|
279次组卷
|
6卷引用:河南省郑州市宇华实验学校2023-2024学年高一下学期4月期中考试数学试题
7 . 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
名校
8 . 已知
外接圆半径为
,
,
为锐角,则下列正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de1d395e6c48c0676a1488a299479d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() |
B.![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
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9 . 在
中,
,
,
边上的中线
,则
的面积S为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c013bbe1fb6e9acf461548b5cf6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e530783dc49238736ed5c1157e6184dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-03-25更新
|
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