如图,在三棱柱
中,侧面
为正方形,侧面
为菱形,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/2ef6705b-4cb0-4c93-8332-2919c906fc73.png?resizew=172)
(1)求直线
与平面
所成角的正弦值;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57eb483244073b76d7acd49feaf18280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce04b35c265cc9c48b60204bd2f718ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/2ef6705b-4cb0-4c93-8332-2919c906fc73.png?resizew=172)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dfb64c679bf4a62e5ee092d8885fc09.png)
更新时间:2020-01-31 23:39:30
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相似题推荐
解答题-作图题
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适中
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【推荐1】如图所示,在三棱柱
中,
,点
在平面
的射影为线段
的中点,侧面
是菱形,过点
、B,D的平面
与棱
交于点E.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/631e9b44-e123-41f6-b1ec-0ec73c275a27.png?resizew=162)
(1)在图中作出截面
,并证明四边形
为矩形;
(2)若
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/631e9b44-e123-41f6-b1ec-0ec73c275a27.png?resizew=162)
(1)在图中作出截面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/202794c51b2166eca170da9c53247bea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/202794c51b2166eca170da9c53247bea.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
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解答题-问答题
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解题方法
【推荐2】如图,在底面为矩形的四棱锥
中,PA⊥底面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/3/d9e02b87-edcb-4288-b7f6-1a71c47877e2.png?resizew=159)
(1)证明:平面PAD⊥平面PCD.
(2)若
E在棱AD上,且
,求PE与平面PBD所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/3/d9e02b87-edcb-4288-b7f6-1a71c47877e2.png?resizew=159)
(1)证明:平面PAD⊥平面PCD.
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f18f775dcfd942885aca1efb439e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be62ac0f5edb1eaebb5f491a7c30f97b.png)
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解答题-问答题
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适中
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【推荐1】如图,四棱柱
的底面ABCD为矩形,
,M为BC中点,平面
,
且
.
![](https://img.xkw.com/dksih/QBM/2021/7/8/2759751327858688/2777755634409472/STEM/d8332bb3-75f6-4e8c-aeb4-2395e64a199e.png?resizew=303)
(1)证明:
.
(2)若此四棱柱的体积为2求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b929269c53a44907dba8ee298a0a522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/849dcb00a09c2e4b5886671140f6d82f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff7ce58deed5cf5c76fd122e9afecfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3232a80d0d71fe3f3f0af470b1aa1a.png)
![](https://img.xkw.com/dksih/QBM/2021/7/8/2759751327858688/2777755634409472/STEM/d8332bb3-75f6-4e8c-aeb4-2395e64a199e.png?resizew=303)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0fda605131780ab8e11cb92ed5295d.png)
(2)若此四棱柱的体积为2求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff420795b334c9934c366b99507d0026.png)
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解答题-证明题
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解题方法
【推荐2】如图,已知四棱锥
的底面为菱形,且
,
,
.
![](https://img.xkw.com/dksih/QBM/2012/7/27/1570941975846912/1570941981491200/STEM/9b1df2a691784cb0bd3eb2b794c12f0f.png?resizew=215)
(
)求证:平面
平面
.
(
)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d82d07acbee5b207c7d053c422868f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fccf1cd8600af23d55876ab14e66e2d4.png)
![](https://img.xkw.com/dksih/QBM/2012/7/27/1570941975846912/1570941981491200/STEM/9b1df2a691784cb0bd3eb2b794c12f0f.png?resizew=215)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde1e200d1dd5ddc433c876c9d2f688c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f323421adf8083d252f0070f54f3a80.png)
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解答题-证明题
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【推荐3】如图:在直三棱柱
中,
,
是棱
的中点,
是
的延长线与
的延长线的交点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/7747a34e-3dde-48bc-928e-d270bc1ac509.png?resizew=207)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
平面
;
(2)求平面
与平面
的夹角的余弦值;
(3)若点
在线段
上,且直线
与平面
所成的角的正弦值为
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a8198f7f6cd914a6b256f0852f3a11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ecad355286188fd317939fa50f9555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/7747a34e-3dde-48bc-928e-d270bc1ac509.png?resizew=207)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a52848aff08399a36f217356007a4b.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc22fde9c06a220f208466c57156409d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
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