1 . 如图,在直三棱柱
中,
,
.
(1)设平面
与平面
的交线为l,判断l与
的位置关系,并证明;
(2)若
与平面
所成的角为
,求三棱锥
内切球的表面积S.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af89996db5c5b01c09a448c8e2e47b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1240a927e5540d2dce76ba019f6cf82.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/7/3650d5da-c50e-4f71-b5f2-8d80f60bd852.png?resizew=162)
(1)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38593653bedb845ecfa820806a29a1e.png)
您最近一年使用:0次
2 . 如图,在四棱锥
中,底面
为正方形,
底面
,
,
为线段
的中点.
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
平面
;
(2)求
与平面
所成角的正切值.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/7/a57eb88d-62d5-4d22-8e3d-207f38660e34.png?resizew=182)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
3 . 如图,在三棱柱
中,
平面
,
,M是AB的中点,
.
;
(2)求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbf225d5b011f6a79642a3def3e05db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
您最近一年使用:0次
2023-07-05更新
|
613次组卷
|
2卷引用:广东省广州市番禺区2022-2023学年高一下学期期末数学试题
解题方法
4 . 三棱锥
中,底面
为正三角形,
平面
,
为棱
的中点,且
(
为正常数).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/6/94d7c905-655d-4532-940a-93cc7eb91911.png?resizew=153)
(1)若
,求二面角
的大小;
(2)记直线
和平面
所成角为
,试用常数
表示
的值,并求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531dd2310518f801ed6160b44d94c236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/6/94d7c905-655d-4532-940a-93cc7eb91911.png?resizew=153)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f88070c5772370fef9c16727145641d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbeab80976db9b4689b9446cda06196a.png)
(2)记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f798a9af75a091a8be0b71f2038260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
解题方法
5 . 如图,直三棱柱
中,
,且平面
平面
.
(1)求BC的长;
(2)求直线AC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/b0b07c9804a4201ed95635c26727401a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/5/c48fafbb-8701-4217-b2f9-17b0fb9364b6.png?resizew=179)
(1)求BC的长;
(2)求直线AC与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
您最近一年使用:0次
解题方法
6 . 如图,在四棱锥
中,DA⊥平面ABE,
,
,
,F是DE的中点.
平面ABE;
(2)若
,直线DE与平面ABE所成角为
,求直线CF与直线DB所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a6f0f2e5bc1f05ed844291b55513da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b547d886c528fa2c63016c217b8fb51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94270844f197d524bf1da4f1385befd2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6164f6484b3b4acafcf1f3fd87ef196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
您最近一年使用:0次
解题方法
7 . 如图,矩形
中,
,
,将
沿直线BD折起至
,点E在线段AB上.
(1)若
平面
,求
的长;
(2)过点P作平面
的垂线,垂足为O,在
折起过程中,点O在
内部(包含边界),求直线
与平面
所成角正弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d649afbddd907f0dfec1420f02f82fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267ace52b64e1e7dfc5211e033255b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee03d4bb4667b6c345221b6c9b0fa4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/5/402e05c3-ca24-4ec3-841e-d1e35d2e7f7e.png?resizew=333)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db807b09cc550f476b3f8fa0c6a14425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(2)过点P作平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
您最近一年使用:0次
2023-07-03更新
|
627次组卷
|
3卷引用:山西省三重教育2022-2023学年高一下学期期末数学试题
山西省三重教育2022-2023学年高一下学期期末数学试题山西省太原市2022-2023学年高一下学期期末数学试题(已下线)第二章 立体几何中的计算 专题一 空间角 微点5 直线与平面所成角综合训练【基础版】
名校
8 . 如图所示,在直三棱柱
中,
,D,E分别为棱AB,
的中点.
(1)证明:CD∥平面
;
(2)求BE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/0619ff7b9845bf3bab5f46f61626c74c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/4/a81ef79b-0f9c-4cc5-aca0-57e4b70aa597.png?resizew=254)
(1)证明:CD∥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
(2)求BE与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
您最近一年使用:0次
2023-07-02更新
|
268次组卷
|
2卷引用:安徽省马鞍山市2022-2023学年高一下学期期末教学质量监测数学试题
9 . 如图,在五面体
中,四边形
为等腰梯形,
,且
.
;
(2)若
为等边三角形,且面
面
,求
与面
所成角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59e89556992cbfd7043330ac7421d342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28d6477c85c5a4ac410a884e92fbe53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee73452ee4d5437f1399f1235b95e55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b66cd5029091a0290fbfd8c7a66dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5f0cfc1049f84a04c81bd213afb8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28d6477c85c5a4ac410a884e92fbe53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
您最近一年使用:0次
2023-07-01更新
|
276次组卷
|
2卷引用:湖北省咸宁市2022-2023学年高一下学期期末数学试题
解题方法
10 . 如图,矩形ABCD是圆柱
的一个轴截面,点E在圆O上(异于A,B),F为DE的中点.
平面
;
(2)若直线DE与平面
所成的角为
时,证明:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f332555e65843f32f4c623098c6adc72.png)
(2)若直线DE与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf84ed033bd035c2fe7552badd5e447d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
您最近一年使用:0次
2023-07-01更新
|
387次组卷
|
2卷引用:湖北省武汉市部分学校联合体2022-2023学年高一下学期期末联考数学试题