名校
解题方法
1 . 如图,在正三棱台
中,
,
,过棱
的截面
与棱
,
分别交于
、
.
(1)记几何体
和正三棱台
的体积分别为
,
,若
,求
的长度;
(2)若
,求直线
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/f54638dd4ebf19815a1333d84e42f927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/21/5500af58-f705-43a1-b87a-20cb2dd9779a.png?resizew=182)
(1)记几何体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae55ec08598586beba0b48f7315e596c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbdd978c1b5c790670e8eac1ca2ae969.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68a44992693cc6bbfa489a59a9e00cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
您最近一年使用:0次
2023-06-20更新
|
273次组卷
|
2卷引用:浙江省衢州市2022-2023学年高二下学期期末数学试题
解题方法
2 . 在矩形
中,
,
,点
为线段
上的中点,沿
将
翻折,使得
,点
在线段
上且满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/19/15806d1c-89e7-4093-902c-bb5cb86c4cb8.png?resizew=204)
(1)证明:平面
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/101da161ae17652ccbe7d3f888762c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69509ad4786945359ce950ad284d0c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d669df6c391aa83150df5ae96c39d8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/19/15806d1c-89e7-4093-902c-bb5cb86c4cb8.png?resizew=204)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e462c38951671d0dbbea78246da9f580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
3 . 如图,在平面四边形
中,
,M在直线
上,
,
,
绕
旋转.
![](https://img.xkw.com/dksih/QBM/2021/2/1/2648790370820096/2650026749878272/STEM/838c09b4-f7ad-4e32-9f49-9d613b46ca22.png)
(1)若
所在平面与
所在平面垂直,求证:
平面
.
(2)若二面角
大小为
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0991d38c6edebb9740ab1061437c720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3fb1c94a174362ba469507cb532afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef76bc37e256a2786bf6b44a32b87110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831b29431c9b0177fa86f841417e89e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/159aa852de7f5b236072c5251669bff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2021/2/1/2648790370820096/2650026749878272/STEM/838c09b4-f7ad-4e32-9f49-9d613b46ca22.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/159aa852de7f5b236072c5251669bff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4e1e8fda90563d2dec09d15e676bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9db7e46fef4f27799aec83a8bfb8eae8.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b954e54a5057567d826beea1791ff362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e663220a66eff19da6a71e46b397db2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3653ada76ba0c8afe9d57c8e7832c6ed.png)
您最近一年使用:0次
解题方法
4 . 如图,四棱台
中,底面
与侧面
为相似的等腰梯形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/81e6cc34-d7ff-4a1e-9e1e-73fa06152f19.png?resizew=188)
(Ⅰ)求证:
平面
;
(Ⅱ)若二面角
的平面角为
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856b7f7d890ea69f5b56f1e041ee0e37.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/81e6cc34-d7ff-4a1e-9e1e-73fa06152f19.png?resizew=188)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a6ca1d6b37072bd7df0cf77737bb79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ef28bae91603373014bff6154c6fc2.png)
(Ⅱ)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b7f8c25db6247cb7bf47c2082926004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ef28bae91603373014bff6154c6fc2.png)
您最近一年使用:0次
名校
解题方法
5 . 如图,在四棱锥
中,
平面
,底面是棱长为
的菱形,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/5784c08c-8831-4e86-9694-ebeba116736d.png?resizew=195)
(1)求证:
//平面
;
(2)求直线
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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c161375e4e6f61f1cbef8083c02e975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/364d6c88726d8c3bb8ed297057332bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/5784c08c-8831-4e86-9694-ebeba116736d.png?resizew=195)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2019-08-02更新
|
1074次组卷
|
4卷引用:【校级联考】浙江省衢州五校2018-2019学年高二第二学期期中联考数学试题
6 . 如图,四棱锥
中,
平面
,
,
,
,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/b6b3c6f4-94fc-46a3-90e1-f23c3dc78deb.png?resizew=172)
(Ⅰ)证明:
平面
;
(Ⅱ)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.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/b37591109b0a0ec5ffe2133f83310eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb8d6911eab97f52e844edc9d2e5ee83.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/2022/12/9/b6b3c6f4-94fc-46a3-90e1-f23c3dc78deb.png?resizew=172)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544381069cb72bed5598ca5adc45ae26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
您最近一年使用:0次
7 . 如图,在正方体
中,点
为线段
的中点.设直线
与平面
成的角为
,则
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec275f823ae17afdba53301fcbd2aa43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86eec8526479272d15bb3b171a46de0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b80751c98f9991b9cfc03923a98834.png)
![](https://img.xkw.com/dksih/QBM/2018/11/15/2076027441364992/2078025456386048/STEM/009c7e0a6eb6449dbb596c92bc31af36.png?resizew=143)
您最近一年使用:0次
8 . 如图,在直三棱柱
中,
,
,且
分别是
中点.
(1)求证:
平面
;
(2)求直线
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/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd8f940b796af67206b3f9dd410a407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44aeeb9447719f64b42aec3916fc0893.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/418162f5ac09aed756c6606d10ebdb3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3ef97d64e58d311019b70fe5e2cc0d.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3ef97d64e58d311019b70fe5e2cc0d.png)
![](https://img.xkw.com/dksih/QBM/2018/2/8/1878170273792000/1879942576128000/STEM/fd47db3f96dd4ffca4a7b6635805358f.png?resizew=151)
您最近一年使用:0次
9 . 如图,在四棱锥
中,侧面
底面
,底面
为矩形,
,
.
(1)求证:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db3940f180ba6947c2edcfaf4431e42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/781c38c2ca51beb16eeebce1f843fe01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b82fa8f506f8099ca06c36c706db479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff50f835a78636c5d0e78a917fd4abb1.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b753d9059ea17319dfa503b6003d6138.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://img.xkw.com/dksih/QBM/2018/5/4/1938155828674560/1939602241552384/STEM/d18f03b5ea254153b50b56d6849a2a66.png?resizew=244)
您最近一年使用:0次
10 . 三棱锥
中,
是
的中点,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/20/136c353c-0136-4ef1-854e-cf692b63c2e5.png?resizew=152)
(1)求证:
;
(2)若二面角
的余弦值为
,求
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.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/2648ba19b620635fef3cb9530de4c84b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6129f9f1fbb9334a10b4dc6c89aebc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/20/136c353c-0136-4ef1-854e-cf692b63c2e5.png?resizew=152)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c51c25b65a37b676ae3c3b71c29f9b.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1854ba6cc92481d7a616bd2788a47e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
您最近一年使用:0次