如图,直角梯形
与等腰直角三角形
所在的平面互相垂直,
.
![](https://img.xkw.com/dksih/QBM/2016/11/28/1573184855162880/1573184861110272/STEM/d01b9e66d8774ad8a08a45513c4aec5e.png)
(1)求直线
与平面
所成角的正弦值;
(2)线段
上是否存在点
,使
平面
?若存在,求出
;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad9a8fd82e14814d1f073b185ded6abd.png)
![](https://img.xkw.com/dksih/QBM/2016/11/28/1573184855162880/1573184861110272/STEM/d01b9e66d8774ad8a08a45513c4aec5e.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e041ba4d0e619ee4545097ee1522a0f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128c69eb81dae89c6989d06d20925ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38757c4b09eddb4b0f3c472f4d90626.png)
更新时间:2016-12-05 01:55:42
|
相似题推荐
解答题-证明题
|
适中
(0.65)
解题方法
【推荐1】如图,在直三棱柱
中,已知
,设
的中点为
,
.求证:
![](https://img.xkw.com/dksih/QBM/2020/8/14/2527831942242304/2530675692716032/STEM/5843b21c-e222-4d2c-8df9-5e1d4f551b9e.png)
(1)
平面
(指出所有大前提、小前提、结论);
(2)
(用分析法证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eec2bbb7272f66c7cf92620da8372d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88b866f54e2c5c1df06364cdc7eb59bc.png)
![](https://img.xkw.com/dksih/QBM/2020/8/14/2527831942242304/2530675692716032/STEM/5843b21c-e222-4d2c-8df9-5e1d4f551b9e.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98faac7a82235d53bb4b6abe7ee54951.png)
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解答题-证明题
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适中
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【推荐2】如图所示,已知四棱锥
中,底面
是矩形,平面
底面
且
为
中点.点P在平面ABCD上的投影在线段AD上.
![](https://img.xkw.com/dksih/QBM/2022/3/15/2936816934264832/2937439182462976/STEM/ac3298a1-0fca-4757-8489-d7c40ca5465e.png?resizew=176)
(1)求证:
;
(2)若
与底面
所成角的正切值为
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8451148a036b44f7248dfaf3fe9096fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2022/3/15/2936816934264832/2937439182462976/STEM/ac3298a1-0fca-4757-8489-d7c40ca5465e.png?resizew=176)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4486d52b6e410fd7b60428121d96cef.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0f73cf7ab0c2a8a0099cb2873c81f4.png)
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【推荐1】如图,矩形
所在的平面与等边
所在的平面垂直,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2015/11/9/1572283446231040/1572283452358656/STEM/783a21cba3034167a023ebf238eaa4d9.png)
(1)求证:
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a73d381aab499a5c0a5e81cee02efd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2015/11/9/1572283446231040/1572283452358656/STEM/783a21cba3034167a023ebf238eaa4d9.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94797c3647d8d188f655772f01864ce.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/114535a0f82dbb18dae843f6f191a87d.png)
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解答题-问答题
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适中
(0.65)
【推荐2】如左图,平面五边形
中,
,
,将△
沿
折起,得到如右图的四棱锥
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/d7db16bd-f00e-4e5e-820d-ccb641492a13.png?resizew=358)
(1)证明:
;
(2)若平面
平面
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a7b0d00cbe53f9bbdb464a1c8c5e59b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e413f89893a9b2e24d2a9d1c00e00f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/d7db16bd-f00e-4e5e-820d-ccb641492a13.png?resizew=358)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ebfe6fda511e39f72ba2519f4da31c9.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2c4cc37d6ba218107c9c5d820740fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
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名校
【推荐3】在三棱锥S-ABC中,△ABC是边长为4的正三角形,平面SAC
⊥平面ABC,SA=SC=2
,M、N分别为AB、SB的中点.
(1)证明:AC⊥SB;
(2)求二面角N-CM-B的正切值大小;
(3)求点B到平面CMN的距离.
⊥平面ABC,SA=SC=2
![](https://img.xkw.com/dksih/QBM/2011/10/14/1570316276137984/1570316282019840/STEM/678c9955517a47f7a3e23c22c64d46e1.png?resizew=24)
(1)证明:AC⊥SB;
(2)求二面角N-CM-B的正切值大小;
(3)求点B到平面CMN的距离.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/14/f19fc19c-5796-4f19-8dec-50ed91a5c8b2.png?resizew=145)
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