如图,在三棱锥
中,
,
,
.求二面角
的平面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7224109389aeea7636f340928655422b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0155f50f2b5c4d960e2e347b0cd90e5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93767331e9bac06a564973a9f4fc663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f17ef2f38ffd644351cfeaae5ccbfd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ed8c47aa921ed197357ad0da7ebe1a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/6/5a91a9a8-803c-47ea-8665-5ae95ec6464a.png?resizew=158)
2023高一·全国·专题练习 查看更多[3]
(已下线)专题强化训练四 直线与平面所成的角、二面角的平面角的常见解法(1)-《考点·题型·技巧》(已下线)专题强化训练四 直线与平面所成的角、二面角的平面角的常见解法(2)-《考点·题型·技巧》(已下线)专题强化二:异面角、线面角、二面角的常见解法 (1)
更新时间:2023-06-02 23:32:45
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解答题-作图题
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解题方法
【推荐1】如图为一块直四棱柱木料,其底面
满足:
,
.
![](https://img.xkw.com/dksih/QBM/2022/1/18/2897002878722048/2926845450665984/STEM/e965b444-13ae-43bd-b609-5f5bac543f48.png?resizew=156)
(1)要经过平面
内的一点
和棱
将木料锯开,在木料表面应该怎样画线?(借助尺规作图,并写出作图说明,无需证明)
(2)若
,
,当点
是矩形
的中心时,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://img.xkw.com/dksih/QBM/2022/1/18/2897002878722048/2926845450665984/STEM/e965b444-13ae-43bd-b609-5f5bac543f48.png?resizew=156)
(1)要经过平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8745717601cd14b46c2298919b41b502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f9660760804ff01bbc9319b7342191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f96c341e13ce6cbbc5975f0ef53001.png)
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解答题-证明题
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【推荐2】如图,
和
都垂直于平面
,
是
上一点,且
,
为等腰直角三角形,且
是斜边
的中点,
与平面
所成的角为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/d8adbf38-85ba-4d6a-b98b-7680ff33e7f3.png?resizew=167)
(1)证明:
平面
;
(2)求二面角
的平面角的正切值;
(3)若点P是平面ADE内一点,且
,设点P到平面ABE的距离为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b1c22e1a7bb01c795b34b0b323ece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/d8adbf38-85ba-4d6a-b98b-7680ff33e7f3.png?resizew=167)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/befd9ccddb75aeb71cd1a008669f34da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395de6d5d6b0073af625ae32a4abf9a1.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1befad21888ca33d1d6be4acbe7bbd95.png)
(3)若点P是平面ADE内一点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026ec361327730d3c614a6f25b9b994f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c002e76ec64a9a1922c93a8a51d48426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a4b32d388558eb9a9e4f0f2dd57c09.png)
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【推荐1】如图①,在矩形
中,
,
,
是
的中点,将三角形
沿
翻折到图②的位置,使得平面
平面
.
![](https://img.xkw.com/dksih/QBM/2017/8/18/1754646360842240/1754918654484480/STEM/e01befc15b094e2583eb073e55d12796.png?resizew=401)
(1)在线段
上确定点
,使得
平面
,并证明;
(2)求
与
所在平面构成的锐二面角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec43f7352b3a8c194b4c37485fb4ffd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/2017/8/18/1754646360842240/1754918654484480/STEM/e01befc15b094e2583eb073e55d12796.png?resizew=401)
(1)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af5d32106d31f3e82f47f579f71b492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350d224711c8773a7c5a2b34bf40bedc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b108af99a988f5cde9fc3cf0868edb0.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4be545e103b79ab78280cebff6345d5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a51ae3e15732c9919ab2d79ba597980.png)
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【推荐2】在三棱柱
中,
是
和
的公垂线段,
与平面
成
角,
,
.
平面
;
(2)求
到平面
的距离;
(3)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05793b74b1498de69bcea331f9d7651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f77f400a3cf0acb19d4e4c7da2b80a7.png)
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【推荐3】如图,四棱锥
中,底面
是直角梯形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b2050ced52081184a6ca55e166d9f3a.png)
平面PBC;
(2)已知
,
,
,若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b2050ced52081184a6ca55e166d9f3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d2bbf2309b4ff8599f57bca4203e90.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07a898421b1752c9ad2293044cd42a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445f7aff0e643af8435fe0676f366850.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a3870ebb0a0e392da7947ac8c5d843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/201caba8e53db5b7d7a64571afa48641.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57d987e01ac3e624bfccfce94628562.png)
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