如图,三棱柱
中,
,
,
,M为
的中点.
平面ABC;
(2)若平面ABC⊥平面
,
,
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d89ba4036a5d18ec4abed44d7fd8e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1baa3d0db9ad31d33c2883a6efed1dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dbd295232d76696f3c98e8328a4f866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
(2)若平面ABC⊥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b29e8a1eefb6776168969a1155c9e9c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d40c4832f8bcb47e57142ba0be2642.png)
更新时间:2024-05-24 16:43:50
|
相似题推荐
解答题-证明题
|
适中
(0.65)
【推荐1】在如图所示的多面体
中,已知
,
,
是正三角形,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2018/2/16/1883773608181760/1888367141494784/STEM/bc500b339b6a44a399b38edefcc1628d.png?resizew=152)
(1)求证:
平面
;
(2)求证:平面
平面
;
(3)求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e20b970f3b0dc1c9a3de6eb09beead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f8f01137e92c0f2e63467036ae9cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d3966314cac2e80fc1a95403310077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19fc9f894312e55c87a0d6737080e233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2018/2/16/1883773608181760/1888367141494784/STEM/bc500b339b6a44a399b38edefcc1628d.png?resizew=152)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d46554105150391e671609fc6348a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39282bdf319f30d7bc261e2e3ab3b1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
名校
解题方法
【推荐2】已知四棱锥
如图所示,其中
,点M,N分别是线段SC,AB的中点.
平面
;
(2)若二面角
为直二面角,则
,
,求四面体SBDM的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f08faa7f1550cb3732de12b2be5fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2adc7cd17def14a434740c702e1cd975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f2acab56e2002173333e27b5738416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1be05bfbcad72d0f9f12a20c4b015c3.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f560374a335e373cbfa8d94816ef2d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
解题方法
【推荐3】在四棱锥
中,底面
为矩形,
平面
为
的中点
(1)证明:
平面
;
(2)证明:
平面
;
(3)若
三棱锥
的体积为
,求点D到平面
的距离.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d11e19c84255eb0431415c2dec553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926584088b939200d88e64318f2d4e6c.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7de1cf3d926cc358360ce3bd35dfa32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfe0ccf24d760c77535a70c92dad145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802e162b98c280720fcb909cf392fda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
名校
解题方法
【推荐1】如图,在三棱台
中,
,
,
,
,
.
平面
;
(2)设
是
的中点,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c1af8d6dbc08e2c61280de54e020af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570f8b295ee0c7c60e6fe1dbf054ff52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a566b100fb2ebe3d208f9b6527934218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e00da418fcef8a1ae5e1472aa99c1228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d97f616f0f32beed421129cbbb4db8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354c20e085fe1a99a8be03bd1d16b2f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df00cdf77ed39ca5a0b305861a693142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb3f0b5d8bf98eeff66f43b7dcbb4be.png)
您最近一年使用:0次
解答题-问答题
|
适中
(0.65)
【推荐2】如图,已知
是以
为底边的等腰三角形,将
绕
转动到
位置,使得平面
平面
,连接
,
,
分别是
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/58d37f15-442a-46c6-8ffb-a4c53ff2699e.png?resizew=159)
(1)证明:
;
(2)在①
,②点
到平面
的距离为3,③直线
与平面
所成的角为60°这三个条件中选择两个作为已知条件,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/58d37f15-442a-46c6-8ffb-a4c53ff2699e.png?resizew=159)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab00e0cff0876c4183a47f1272cf9928.png)
(2)在①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a91b9b3cfe2e5504238b8b7eeea7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b051f51b7d4ce0a3a6d0b7eb880a2fbf.png)
您最近一年使用:0次
解答题-证明题
|
适中
(0.65)
【推荐3】在如图所示的几何体中,四边形
为平行四边形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88046132c9706a26c511bfb55fb8f681.png)
,
⊥平面
,
,
,
.
(1)若
是线段
的中点,求证:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88046132c9706a26c511bfb55fb8f681.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95f3c91c4d56870850ce47c7c7844bc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/058f36d315245b63a811d5c6f348c17b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdd2e599ebb7a0a1c13a0b4b228f5156.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d240d08f5ad81fb1d597546038ea66d5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb4ed9cc8de27b406740fa3e4d5ab73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b820c84570da9c38d0a81c22788b76.png)
![](https://img.xkw.com/dksih/QBM/2012/2/20/1570755401695232/1570755406880768/STEM/b5c41fb960b64f79b46aeaebc349c892.png?resizew=288)
您最近一年使用:0次