名校
解题方法
1 . 元荡湖位于长三角一体化示范区内,2018年青浦㨦手吴江启动实施了元荡生态岸线整治,2023年8月实现元荡青浦段岸线全线贯通.如图,为拓展旅游业务,现准备在元荡湖边建造一个观景台
,已知射线
,
为元荡湖两边夹角为
的公路(长度均超过2千米),在两条公路
,
上分别设立游客接送点
,
,从观景台
到
,
建造两条观光线路
,
,测得
千米,
千米.
的长度;
(2)若
,求两条观光线路
与
之和的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810fee760e06028fb7d37e65db79bfa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c65312db84bbe37e0e1b400bf78c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add60595ecea5d00ff1fbb2a5409be73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
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2 . 如图、某港口O要将一件重要物品用小艇送到一艘正在航行的轮船上,在小艇出发时,轮船位于港口O北偏西
方向且与该港口相距
的A处,并以
的航行速度沿正东方向匀速行驶,假设该小艇沿直线方向以
的航行速度匀速行驶,经过
与轮船相遇.(假设水面平静)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/19/6b7939b6-56a3-4ae7-90d0-7b6d0d796451.png?resizew=168)
(1)要使相遇时小艇的航行距离最短,小艇的航行速度应为多少?
(2)假设小艇的速度最快只能达到
,要使小艇最快与轮船相遇,应向哪个方向航行?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d1525355976915a23b0a3050e6a687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdde1bd791be76f4dfc0116f5c8dacce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6737e5a65b0067db9bdac02a52de7131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ee630252dc9ec9c8453d1561a81743.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/6/19/6b7939b6-56a3-4ae7-90d0-7b6d0d796451.png?resizew=168)
(1)要使相遇时小艇的航行距离最短,小艇的航行速度应为多少?
(2)假设小艇的速度最快只能达到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d568215783a27afd4041395551623c4a.png)
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4卷引用:陕西省渭南市富平县蓝光中学2023-2024学年高一下学期6月月考数学试题
陕西省渭南市富平县蓝光中学2023-2024学年高一下学期6月月考数学试题云南省曲靖市部分学校2023-2024学年高一下学期6月联考数学试题辽宁省朝阳市建平县第二高级中学2023-2024学年高一下学期6月月考数学试题(已下线)专题1 以实际问题为背景的解三角形问题【讲】(高一期末压轴专项)
3 . 如图,某大型厂区有三个值班室
,值班室
在值班室
的正北方向3千米处,值班室
在值班室
的正东方向4千米处,仓库
在
边上且满足
.
到值班室
的距离;
(2)保安甲沿
从值班室
出发行前往值班室
,保安乙沿
从值班室
出发行前往值班室
,甲乙同时出发,甲的速度为
,乙的速度为
.若甲乙两人通过对讲机联系,对讲机在厂区内的最大通话距离不大于3千米,请问有多长时间两人不能通话?
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942a9a6bde4a5b9803b68b1e9065de62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)保安甲沿
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.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/f52a58fbaf4fea03567e88a9f0f6e37e.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/3b1dfb863105600ca271cd6a597187ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15bca4fc0b0fc4f8e492d8c1fe449c9b.png)
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解题方法
4 . 已知a,b,c分别为
内角A,B,C的对边,下面四个结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.若![]() ![]() |
B.在锐角![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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2卷引用:吉林省实验中学2023-2024学年高一下学期5月期中考试数学试题
解题方法
5 . 在
中,角
的对边分别是
,已知
,点
在边
上,
是内角
的角平分线,且
,则
面积的最小值是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc7eb7c88b487f83ce1a3573505c6d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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6 .
的面积为
,角
的对边分别为
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f46d8ed9e119eb8036096755fb74a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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7 . 作为一种新的出游方式,近郊露营在疫情之后成为市民休闲度假的“新风尚”.我市城市规划管理局拟将近郊的一直角三角形区域按如图所示规划成三个功能区:
区域为自由活动区,
区域规划为小型鱼塘养鱼供休闲垂钓,
区域规划供游客餐饮休息用.为安全起见,预在鱼塘
四周围筑护栏.已知
,
,
,
.
时,求护栏的长度(
的周长);
(2)若鱼塘
的面积是“餐饮休息区”
的面积的
倍,求
;
(3)当
为何值时,鱼塘
的面积最小,最小面积是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cee975a18902203254aa21d541c671f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e856c15c61d7cb6ebd8daef542a4e7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f30bb9fbf908f410572cd8e1aea0b21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e856c15c61d7cb6ebd8daef542a4e7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b5854b6521f9f19659429add18ac058.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3bc8fd3cb142574f9efd73deca8dbff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5cf48407af008db11eb4f236691d741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc798f8db4d63d1734e7f47740a5793.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e856c15c61d7cb6ebd8daef542a4e7f.png)
(2)若鱼塘
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e856c15c61d7cb6ebd8daef542a4e7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f30bb9fbf908f410572cd8e1aea0b21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e520cef3cebf757a24737ffb661834.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e520cef3cebf757a24737ffb661834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e856c15c61d7cb6ebd8daef542a4e7f.png)
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3卷引用:江苏省五市十一校2023-2024学年高一下学期5月阶段联测数学试卷
江苏省五市十一校2023-2024学年高一下学期5月阶段联测数学试卷福建省厦门外国语学校2023-2024学年高一下学期第二次月考数学试卷(已下线)专题1 以实际问题为背景的解三角形问题【练】(高一期末压轴专项)
8 . 如图,为了测量两山顶
间的距离,
四点在同一铅锤平面内,飞机沿水平方向在
两点进行测量,途中在点
测得
,在点
测得
,测得
.
和点
之间的距离;
(2)求两山顶
间的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea2c16ef76fc4a94fd96cd2235f2738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35615a66efc683ffff95b67e9ebbcbf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e322e85c644d721b4082b9894fd80d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ac9bee47fa0dcd86158c9f18547725c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb27f71b7236edb4924864a535d4204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)求两山顶
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
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解题方法
9 .
的内角A,B,C的对边分别为a,b,c,已知
,
,
,则边
的值是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c30701144de929b875643ec466889f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c7895a304fbb8bfecb2cd72ab9f280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03699cf3aa154fd75501ae7388d2539c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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解题方法
10 . 在
中,角A,B,C所对的边分别为a,b,c,下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.若![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() |
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