如图,某小区准备将闲置的一直角三角形地块开发成公共绿地,图中
,
,
.设计时要求绿地部分(如图中阴影部分所示)有公共绿地走道
,且两边是两个关于走道
对称的三角形(
和
).现考虑绿地最大化原则,要求点
与点
,
均不重合,
落在边
上且不与端点
,
重合.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/241bbd3b-af4f-4c68-a6d3-84219a4a6ac9.png?resizew=211)
(1)设
,若
,求此时公共绿地的面积;
(2)为方便小区居民的行走,设计时要求
,
的长度最短,求此时绿地公共走道
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60ae4577cbc7f96e065f0557bc0d0df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc6b94f23607ff4261c371ec9425c8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae963ba456d7bb2a83fd7082582bbf26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7f58eeb3fb122d2b8ebe6b2b44acdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/241bbd3b-af4f-4c68-a6d3-84219a4a6ac9.png?resizew=211)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e31cf7ea7942bbc0fe4680878e5dd2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc1f08c7640e62e8717abf4d44a6c83.png)
(2)为方便小区居民的行走,设计时要求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebad23f7992ba222ddc115f1458065f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
更新时间:2021-08-24 16:57:49
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适中
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名校
【推荐1】如图,
是直角三角形,
,
,D为边
上一点,且
,
.
![](https://img.xkw.com/dksih/QBM/2020/8/5/2521507675095040/2522494434304000/STEM/6beb2ee9-339d-4e7e-b748-24336bbb0f71.png)
(1)求
的长:
(2)求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98aa2d95ef06695d19891a4b198e6233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a74c3e9a8f3f11e98b4fa659a97679.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46571701ccaa18d3c844ab99ee6c30e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6964b99181d039fe8c5ed5fe2bb00f1.png)
![](https://img.xkw.com/dksih/QBM/2020/8/5/2521507675095040/2522494434304000/STEM/6beb2ee9-339d-4e7e-b748-24336bbb0f71.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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【推荐2】在△
中,角
,
,
所对的边分别为
,
,
,已知
,
.
(1)若
,求△
的面积;
(2)若
,点
为
中点,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/9cbec6432d2fc264cb3e9654f14bec05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d0d3572d9890f9bbd07797494763a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7fa79a550591eb9e1bd07bced3a08fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
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解题方法
【推荐1】在△
中,内角
的对边分别为
,且
.
(1)求C;
(2)若
,
,△
的面积为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/e23061ee21f807d7b8ac211596d84c10.png)
(1)求C;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/036b23c94e305faaa1283996edc5b30c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb57d84f9bbcb3e30d4ce7e2e1e8604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e24361e4842cdaa3da819c60b55107d7.png)
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【推荐2】在锐角
中,
三内角所对的边分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7132c2d8b2ff504e6c2ba36c4f6dcfaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2132c575dc0b845dcea96da2ff819ce.png)
.
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802a504b0490c9a9fdb2eed1fb93b73f.png)
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3470f8e8142a61cfd3d4aa1e1e203d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7132c2d8b2ff504e6c2ba36c4f6dcfaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2132c575dc0b845dcea96da2ff819ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/783d6adfa8fb1352679c5185258d842a.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802a504b0490c9a9fdb2eed1fb93b73f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/052eb57d83181988130a458d21b3950f.png)
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【推荐1】位于灯塔
处正西方向相距
的
处有一艘甲船,需要海上加油.位于灯塔
处北偏东
有一与灯塔
相距
的乙船(在
处).求乙船前往支援
处的甲船航行的距离和方向(角度精确到
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d8fe32e5c525b1143c7d2c80a523b2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/306adb78d8090d7c94e4b824ddc90eb6.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/a840804ee07144f46c9c2a33e33ae450.png)
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【推荐2】已知海岛B在海岛A北偏东
,A,B相距10海里,游船甲从海岛B以1海里/小时的速度沿直线向海岛A行驶,同时游船乙从海岛A沿着北偏西
方向以2海里/小时的速度行驶.
![](https://img.xkw.com/dksih/QBM/2021/3/24/2684666206896128/2687147581595648/STEM/eb5ebc74-5cd6-4644-a8c1-2af62e1f8ff5.png?resizew=158)
(1)问经过多长时间,游船甲在游船乙的正东方向;
(2)求游船甲从海岛B驶向海岛A的过程中,甲、乙两船间距离的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c12e76fbd84eeec721386bd3b04cc4.png)
![](https://img.xkw.com/dksih/QBM/2021/3/24/2684666206896128/2687147581595648/STEM/eb5ebc74-5cd6-4644-a8c1-2af62e1f8ff5.png?resizew=158)
(1)问经过多长时间,游船甲在游船乙的正东方向;
(2)求游船甲从海岛B驶向海岛A的过程中,甲、乙两船间距离的最小值.
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【推荐1】如图,在
中,已知
,点
、
在射线
运动(不含端点,且
),点
在射线
上且
,且
.
![](https://img.xkw.com/dksih/QBM/2021/5/7/2716000481984512/2784649413378048/STEM/0d2a1d2f-9064-449c-86f2-bf63fdb88907.png)
(1)若
,求
长;
(2)当
、
在射线
运动时,设
,记
的面积为
,求
的解析式,并求出
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1eb76fe74cba30f7cbcde349ba80da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0400ac38763d89b8e0a90db313f62876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07445aa3909818a3ef93bb01182f545f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54baded1253f82e27e498c76cf58a1fa.png)
![](https://img.xkw.com/dksih/QBM/2021/5/7/2716000481984512/2784649413378048/STEM/0d2a1d2f-9064-449c-86f2-bf63fdb88907.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/863544b6162ca5c8bc38ade2fc28f8a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b911a96a6cb756da8ace9902c97ef68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b51d3992644d37dc71c9b5a97d515c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe3c32177de03f8413f85d4a16ff647f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe3c32177de03f8413f85d4a16ff647f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe3c32177de03f8413f85d4a16ff647f.png)
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【推荐2】记
ABC的内角A,B,C的对边分别为a,b,c,已知
,且
.
(1)若
ABC的面积为
,求b;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c01e3f34a29ad8239d28abe55c86d3d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ba9d5fe5d6b66b0230ea497c4c5583.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbb5a9c67bbafe405f3149596baf960c.png)
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