1 . 古时候,为了防盗、防火的需要,在两边对峙着高墙深院的“风火巷”里常有梯子、铜锣、绳索等基本装备.如图,梯子的长度为
,梯脚落在巷中的
点,当梯子的顶端放到右边墙上的
点时,距地面的高度是
,梯子的倾斜角正好是
,当梯子顶端放到左边墙上的
点时,距地面的高度为6尺(1米=3尺),此时梯子的倾斜角是
.则小巷的宽度
等于 ( )
![](https://img.xkw.com/dksih/QBM/2022/11/1/3100452787003392/3100529466490880/STEM/8f00d8fc8e21487d86bcd145f3ac7f29.png?resizew=189)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.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/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c12aeebfa1af16f325c98a43bb08c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2022/11/1/3100452787003392/3100529466490880/STEM/8f00d8fc8e21487d86bcd145f3ac7f29.png?resizew=189)
A.6尺 | B.![]() | C.(![]() | D.![]() |
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2 . 深圳别称“鹏城”,是中国的窗口,“深圳之光”摩天轮是中国之眼,如图(1),代表着开拓创新、包容开放的精神,向世界展示着中国自信,摩天轮的半径为6(单位:10m),圆心O在水平地面上的射影点为A,摩天轮上任意一点P在水平地面上的射影点都在直线l上,水平地面上有三个观景点B、C、D,如图(2)所示,其中在三角形ABC中,
,
,
,
,
,记
(单位:10m).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/82138544-e1b4-41ad-8a8e-dd8dde0f6a0e.png?resizew=344)
(1)求
的值;
(2)因安全因素考虑,观景点B与摩天轮上任意一点P的之间距离不超过
(单位:10m),求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5a97e6b884fb4ad12e62f77092d0e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6037bba27008abc96a6dba99753549ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253c6a4ac9d325987854abe00a0e0b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efbaf0f7253cfb0178d99aaa7d2a0b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30fbeb2f1f6ee7279885520d889bfc47.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/82138544-e1b4-41ad-8a8e-dd8dde0f6a0e.png?resizew=344)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d54d09ef825305de83671448a3dea21.png)
(2)因安全因素考虑,观景点B与摩天轮上任意一点P的之间距离不超过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e34f0569c29c26530dd7b394a6ec51.png)
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2021-11-20更新
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3卷引用:江苏省淮阴中学、海门中学、姜堰中学2021-2022学年高三上学期期中联考数学试题