名校
解题方法
1 . 某广场一雕塑造型结构如图所示,最上层是一呈水平状态的圆环,其半径为
,通过金属杆
,
,
,
支撑在地面
处(
垂直于水平面),
,
,
是圆环上的三等分点,圆环所在的水平面距地面
属杆
,
,
所在直线与圆环所在水平面所成的角都为
.(圆环及金属杆均不计粗细)
![](https://img.xkw.com/dksih/QBM/2021/4/29/2710163069018112/2798947815768064/STEM/21808899dc1041548d9a25a6be5d21c5.png?resizew=156)
(1)当
的正弦值为多少时,金属杆
,
,
,
的总长最短?
(2)为美观与安全,在圆环上设置
,
,…,
个等分点,并仍按上面方法连接,若还要求金属杆
,
,
,…,
的总长最短,对比(1)中
点位置,此时
点将会上移还是下移,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71a41641aa0d0e45a3c03d3d2c1196b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabe764f05300ac83c7d16b685d27af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae3a47e231dcbb00667109b40722bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287d8edca8efb868f5233c19e2e9edb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167e6e41ac221847824a72e964f340f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabe764f05300ac83c7d16b685d27af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae3a47e231dcbb00667109b40722bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287d8edca8efb868f5233c19e2e9edb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/2021/4/29/2710163069018112/2798947815768064/STEM/21808899dc1041548d9a25a6be5d21c5.png?resizew=156)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabe764f05300ac83c7d16b685d27af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae3a47e231dcbb00667109b40722bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287d8edca8efb868f5233c19e2e9edb0.png)
(2)为美观与安全,在圆环上设置
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1093302106aaafb7e197d06fefd01125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabe764f05300ac83c7d16b685d27af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae3a47e231dcbb00667109b40722bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5079f6411c584d0601ab83ca8dea00d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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