名校
1 . 在△ABC中,角A、B、C所对的边分别为a、b、c,且a=6,b=14,
.
(1)求sinA的值和△ABC外接圆半径;
(2)求△ABC的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5f230e4b90954a11db30652d9efeb4.png)
(1)求sinA的值和△ABC外接圆半径;
(2)求△ABC的面积.
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2 . 如图,测量河对岸的塔高AB时,可以选与塔底B在同一水平面内的两个测点C与D,测得∠BCD
,
,
米,并在点C测得塔顶A的仰角为
,则塔高AB为___________ 米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd81657e13368e335720ab0baf861d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c49a35146eec0090b1269283829984bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2aea5dc133fdded83d5453ee447deff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://img.xkw.com/dksih/QBM/2021/5/13/2720395434917888/2800990358544384/STEM/8b909dd2c55a46c8910c1c4fe1925657.png?resizew=242)
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3 . 如图,折线
为海岸线,
km,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/bda86beb-0c42-4a02-8d94-b900036393cc.png?resizew=129)
(1)求
的长度;
(2)若
km,求D到海岸线
的最短距离. (以上答案都精确到0.001km)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0cc6293cfedec30b124ece908c4c438.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33fb0b06f176e59dbe20f17a94a68c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0c8008edad41d576b44024532c83a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd893bb2f4c04219678d9cea126a240d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae916162e4654626a8f8090e856f5af.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/bda86beb-0c42-4a02-8d94-b900036393cc.png?resizew=129)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd4997da49b3dfe98144ad13aed0d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0cc6293cfedec30b124ece908c4c438.png)
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2021-12-12更新
|
332次组卷
|
2卷引用:上海市位育中学2019-2020学年高一下学期期中数学试题
名校
4 .
中,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c13fadefec9d4bad9149b6d5cd3e0e.png)
_______________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1466856bf2570685d3629c1f813748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c13fadefec9d4bad9149b6d5cd3e0e.png)
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名校
解题方法
5 . 在路边安装路灯,灯柱AB与地面垂直(满足∠BAD=90°),且∠ABC=120°,路灯C锥形灯罩,射出的光线如图中阴影部分所示,已知∠ACD=60°,路宽AD=24米,设灯柱高AB=h米,∠ACB=
(30°≤
≤45°).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/0bc34220-4150-4d66-b183-c138d0c824a1.png?resizew=164)
(1)当
=30°时,求四边形ABCD的面积;
(2)求灯柱的高h(用
表示);
(3)若灯杆BC与灯柱AB所用材料相同,记此用料长度和为S,求S关于
的函数表达式,并求出S的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/0bc34220-4150-4d66-b183-c138d0c824a1.png?resizew=164)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)求灯柱的高h(用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(3)若灯杆BC与灯柱AB所用材料相同,记此用料长度和为S,求S关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
2021-07-25更新
|
274次组卷
|
2卷引用:上海市行知中学2020-2021学年高一下学期期中数学试题
名校
6 . 设
(
),若函数
的图像相邻两条对称轴之间的距离为
.
(1)求
的值及函数
的增区间;
(2)在△
中,
、
、
分别是角
、
、
的对边,若
,
,
,求角
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff7866d7c023020ba71be45f619db10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)在△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/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/f8120119749d4bc28067e73fca7d46cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71812e0762c0aaffb51cfef66156567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de6e1389b87a903f0cd149bf2bac4f0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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名校
解题方法
7 . 在锐角△
中,
、
、
分别是角
、
、
所对的边,若
,则
的取值范围为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/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/f256033e3c374cc221304ee9132e4d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25edcc950d3354ff7df6c74dd4d3f3b1.png)
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解题方法
8 . (1)如图,在直径为
的轮子上有一长为
的弦,
是弦的中点,轮子以4弧度/秒的速度旋转,求点
经过
所转过的弧长;
(2)在
中,已知
,
且最长边为1,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb26c5cdef6f16f4b39cd091041b439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd6f4250ca6b1b9bce234a01f00d44d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b478ba1b6261503cf48643e8ddb5c4b.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da34ca79dff70e12ee89de5a28673b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f86b0835b4360ba6c7f90bcf4b7490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/018de3d2-bb2c-4b2e-99f9-95845978d5cc.png?resizew=135)
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解题方法
9 . 如图所示,在河对岸有两座垂直于地面的高塔
和
.小明在只有量角器(可以测量从测量人出发的两条射线的夹角)和直尺(可测量步行可抵达的两点之间的直线距离)且不渡过河的条件下,为了计算塔
的高度,他在点
测得点
的仰角为
,
,又选择了相距100米的
点,测得
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/6f052b58-b2b1-4061-8d80-b68fdc88b36d.png?resizew=185)
(1)请你根据小明的测量数据求出塔
高度;
(2)在完成(1)的任务后,小明想要计算两塔顶之间的距离
,在测得
之后,小明准备再测量两个角的大小,并为此准备了如下四个方案:
方案①:测量
和
方案②:测量
和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e31edc5b71c488ca9942d70d9298f01.png)
方案③:测量
和
方案④:测量
和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36719f1e764ee0e719b65c49fae84677.png)
请问:小明的备选方案中有哪些是可行的?写出所有可行方案的序号;
(3)选择(2)中的一种方案,并结合以下数据,计算出两塔顶
之间的距离,精确到米.
,
,
,
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7142383d6de5773d8be46e6f98cb4ac0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/6f052b58-b2b1-4061-8d80-b68fdc88b36d.png?resizew=185)
(1)请你根据小明的测量数据求出塔
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)在完成(1)的任务后,小明想要计算两塔顶之间的距离
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e94dacf9ef98c98de9344a77079cf5.png)
方案①:测量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d786ee723231d4ca87eb9d011a378b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c36ff76f9f1ee12db562cde7a58b8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cfc2771aa0d5b97d2297f8a26a6f6b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e31edc5b71c488ca9942d70d9298f01.png)
方案③:测量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cfc2771aa0d5b97d2297f8a26a6f6b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb3748300134501953d6b1c3a905026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d786ee723231d4ca87eb9d011a378b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36719f1e764ee0e719b65c49fae84677.png)
请问:小明的备选方案中有哪些是可行的?写出所有可行方案的序号;
(3)选择(2)中的一种方案,并结合以下数据,计算出两塔顶
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7cfbcdbb5fdd552563b0d6fb40a575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ade009e169085eabc56e007e55cfbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa17d54f4bf94ee512f197b15d989223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/493c9cd7c87c96a5f9d2157302b3ede6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f93ac836bfccc1a02cb23921d67c9e16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee04584aacca686baedbbc9eea6d7478.png)
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2021-07-19更新
|
299次组卷
|
3卷引用:上海市浦东新区高桥中学2022届高三上学期期中数学试题
名校
解题方法
10 . (1)证明:
;
(2)
的内角A,B,C所对的边分别为a,b,c,若
,求
的面积S.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad685a7bf2c46a7885168ded59821e5.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6e7abb341272d8653f2b57b0ad3ac2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次