在正方体
中,
是
的中点.
与
所成的角的大小;
(2)求直线
与平面
所成的角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
更新时间:2021-09-06 14:32:07
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相似题推荐
解答题-问答题
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【推荐1】已知四棱锥
中,底面
为直角梯形,
平面
,侧面
是等腰直角三角形,
,
,点
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/2018/3/6/1896263463854080/1898020532232192/STEM/3833b68a9f4d495e809ce3023ccbd8b1.png?resizew=193)
(1)求异面直线
与
所成角的大小;
(2)证明:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.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/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46652d89aa6d3f689edab8628707fed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/620e0bfcd39a05c381524e60236ff3c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/2018/3/6/1896263463854080/1898020532232192/STEM/3833b68a9f4d495e809ce3023ccbd8b1.png?resizew=193)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec43f7352b3a8c194b4c37485fb4ffd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
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解题方法
【推荐2】在直三棱柱
中,
,
,
,D是
的中点.
平面
;
(2)求异面直线
与
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4622aff92fac94916af14f0e913e021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cb62f4c1e0e023619922eb8a509c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc7e774e4ae40c23bf4ceed179230ca.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
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【推荐1】如图,底面是矩形的直棱柱
中,
;
![](https://img.xkw.com/dksih/QBM/2022/1/6/2888391935172608/2889231532441600/STEM/f2c23f6dcf444a879e113d08b91ba2c8.png?resizew=199)
(1)求证:
平面
;
(2)求直线
与平面
所成角的大小;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/864fb23f308b88ee67ab5a0dbc6f9d54.png)
![](https://img.xkw.com/dksih/QBM/2022/1/6/2888391935172608/2889231532441600/STEM/f2c23f6dcf444a879e113d08b91ba2c8.png?resizew=199)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffad41268b4ddbad84b6d6b207b3939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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【推荐2】已知斜三棱柱
的底面是直角三角形,
,侧棱与底面所成角为
,点
在底面上射影
落在
上.
(Ⅰ)求证:
平面
;
(Ⅱ)若点
恰为
中点,且
,求
的大小;
(III)若
,且当
时,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80969d2b85b57d776a482dde2df0f5a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8e21dfb8c59897bb073cdc0b0dc7ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a1ee2ea56b649946ca15c7a9ca0755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57e1abac2c301863b08dba67bbee4b46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7909220d1db380634534190b662ee0a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c72171ccd9796fbb7b493a2d927a39.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161bc8727a789e42bf3f21f401d231b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c69a9fd3fa24e54c9ac3a44a61dc92eb.png)
(Ⅱ)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7909220d1db380634534190b662ee0a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c72171ccd9796fbb7b493a2d927a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50ec41d776c0955beba59a61babd548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a1ee2ea56b649946ca15c7a9ca0755.png)
(III)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9512aaea6156038faaffee9bcba4b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f03a0b1fd25b993a512cae45e52b300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/785151ca88e30fe5f524af2659157a6d.png)
![](https://img.xkw.com/dksih/QBM/2012/2/11/1570729985384448/1570729990782976/STEM/f438f49d787242088954211c690c7852.png?resizew=199)
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【推荐3】如图,在四棱锥
中,底面ABCD为矩形,
,点E为线段PC的中点,且
.
;
(2)求直线PB与平面ADE所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316685631676ce839da7ced55501b2cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4999d4fbcbe15f78c29d518f25d317c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2951b9f77413d5f062acb300b09de1f6.png)
(2)求直线PB与平面ADE所成角的正弦值.
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