如图,已知
是圆锥
的底面直径,
是底面圆心,
,
,
是母线
的中点,
是底面圆周上一点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/ea247f96-59aa-4712-8481-12ab30920482.png?resizew=137)
(1)求直线
与底面所成的角的大小;
(2)求异面直线
与
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb3a4a1f748251e3a5232aec3f40e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79684a6e92297749c005e2b23cac9710.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/ea247f96-59aa-4712-8481-12ab30920482.png?resizew=137)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
18-19高二下·上海青浦·期末 查看更多[2]
更新时间:2019-12-11 17:34:45
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相似题推荐
解答题-问答题
|
适中
(0.65)
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解题方法
【推荐1】如图,直三棱柱
中,
,
,
,点
为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/41dfe9b3-c467-4314-9ed8-3d727535272b.png?resizew=96)
(1)求三棱锥
的体积;
(2)求异面直线
与
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883fc5e3faf39829d60804b59deb1730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354c20e085fe1a99a8be03bd1d16b2f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/41dfe9b3-c467-4314-9ed8-3d727535272b.png?resizew=96)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38593653bedb845ecfa820806a29a1e.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
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【推荐2】如图,空间四边形
中,
,
,平行于
与
的截面分别交
、
、
、
于点
、
、
、
.
![](https://img.xkw.com/dksih/QBM/2020/12/20/2618135299375104/2619158890577920/STEM/86c23ec6-0e48-4a62-9c4a-228dc78b4666.png)
(1)求证:四边形
是平行四边形;
(2)若
,求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae635f678849f902970e6a6374f1c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a892f52fdf020016af8f4b9716017718.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://img.xkw.com/dksih/QBM/2020/12/20/2618135299375104/2619158890577920/STEM/86c23ec6-0e48-4a62-9c4a-228dc78b4666.png)
(1)求证:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c32ffe9f4c7aab691c39afda34ea234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
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【推荐3】如图.在四棱锥
中,已知底面
为矩形,侧面
是正三角形,面
底面
,
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/28/14b8f045-1a15-418a-8853-543a766acd78.png?resizew=178)
(1)证明:
;
(2)若
,且二面角
的大小为
,求异面直线
与
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/852aabd89edffc1b94344ff3f1f31ccd.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/28/14b8f045-1a15-418a-8853-543a766acd78.png?resizew=178)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a52818f1e8b7c27f207abae182a64d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a8e0c5bcf2d86726cd9f561b8ff5fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
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【推荐1】已知三棱锥
中,
平面
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54ed455a3442f6c8bd747fe4655e685d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45bcd8f6ede8cc2513ad41402f40086.png)
(1)求直线
与平面
所成的角的大小;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54ed455a3442f6c8bd747fe4655e685d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45bcd8f6ede8cc2513ad41402f40086.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/83932f82-6b43-450d-8533-c95941adb0c3.png?resizew=128)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e820aec9c1a975242fe6d76408a9cde8.png)
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解题方法
【推荐2】如图,在四棱锥
中,
底面
,
,
,
,E为棱CD的中点.
![](https://img.xkw.com/dksih/QBM/2022/3/3/2928293731328000/2936796197748736/STEM/ab0a4e5aeecc4423b52416dc3351a20f.png?resizew=231)
(1)求直线PD与平面PBE所成角的正弦值;
(2)M为直线PA上一点,且满足
平面PBE,求线段DM的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d730ae4307db56b47849c3a19dedfb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8277767aa2d4369a8c2deb6d16f08d.png)
![](https://img.xkw.com/dksih/QBM/2022/3/3/2928293731328000/2936796197748736/STEM/ab0a4e5aeecc4423b52416dc3351a20f.png?resizew=231)
(1)求直线PD与平面PBE所成角的正弦值;
(2)M为直线PA上一点,且满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcfacd208d769d01f1d4ef20313cd869.png)
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【推荐3】如图,在三棱柱
中,侧面
为菱形,
为
的中点,
为等腰直角三角形,
,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/1fb2883e-2c74-4026-84db-2ae5d32e86d6.png?resizew=193)
(1)证明:
平面
.
(2)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/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ba5383e768dc86e1bfd79c10f96f4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4357216fbd755327c16ef5cb9803b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2919a662cb6d59eac9aa5cdd69dac847.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/1fb2883e-2c74-4026-84db-2ae5d32e86d6.png?resizew=193)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
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