组卷网>知识点选题>三角恒等变换与解三角形结合问题
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1 . 依据《齐齐哈尔市城市总体规划(2011﹣2020)》,拟将我市建设成生态园林城、装备工业基地、绿色食品之都、历史文化名城.计划将图中四边形区域eqId58a45d8f70474d8f94ea62d64c7c1815建成生态园林城,eqId34c6b6e427744abfb88dc90b8c7c2111eqId66d409c343f04cfda647f9bfc7da6b2aeqId1a0830891ff846de8422ea80714ecab4eqId6233efafde5f440d81b3b336d74a9f3a为主要道路(不考虑宽度).已知eqIdbe4dd38b18fa4f60b7e0b76c3dbad1c9eqId600f176283414af29256f07a50edace1eqIdbe60f08f30f94b7c83267aacda6e9fd2km.
说明: figure
(1)求道路eqIddf1e9cfeb6244d738f15ed5ee41bce72的长度;
(2)如图所示,要建立一个观测站eqId052844cae8574a8ab842c38a039baac0,并使得eqId5bdb3d41ed484e038a484d09617600aaeqId01b75aa2d4cc4207b5094ec1ae877cb5,求eqId99a3187c2b8f4bcc9703c74c3b72f1f3两地的最大距离.
2 . 如图,在eqId64b9b599fdb6481e9f8d9a94c102300b中,eqId6e82d3b62ac24ed5b35425ee7b513530eqId7db59ee2d8b6472da74cab63c05de022eqIdbedf755e0fdb4d078d6859360706b163eqId64b9b599fdb6481e9f8d9a94c102300b内一动点,eqIdeba1eb09623444c5be59ac0a0f5b090e,则eqId64b9b599fdb6481e9f8d9a94c102300b的外接圆半径eqIdd9026ce1966847eb86a5e13345fed583=______eqId6dc069fc1fa74d889be09b5324e7e625的最小值为____________
说明: figure
3 . 已知矩形eqId5ce7a06ae7a34393b92b5277978ac014中,eqId069c2488beca46268c69c794496758d0.设点eqId8754ce8cf7f34f04abb9a0c041f57f5c关于eqIdcf2da96900c948a1b3ce7cbfd420c080的对称点为eqId3c4ef2fb042d4b55b89d310b674f9e06eqId507464ec6bd24c0fa037f41eece83cd2eqId34c6b6e427744abfb88dc90b8c7c2111交于点eqIdbedf755e0fdb4d078d6859360706b163,若eqId6334f77dfc7f44d9a8898c93aa6618e5,设eqIda6789a8a73574bf7a0dc9e9340040b0f,则求eqId1ea55ca44e4e48109975325acfa5e7ff的值
说明: figure
解答题 | 一般(0.65) | 2021·全国
4 . 已知eqId64b9b599fdb6481e9f8d9a94c102300b的内角eqId10bbe48f886a4fa78fdf8c1fd064f9b4的对应边分别为eqId0c35b978906247db94f863bbb4eccb90,且eqIdbf5b81c651774ab2ba40788e4dddbf40.
说明: figure
(1)求eqId052844cae8574a8ab842c38a039baac0
(2)设eqId312ef2c826304089b9b0f1d1e88b0f50eqId0627be51821d4be7b3e024a354815d64边上一点﹐且eqId01516743b2464cadb1b3a77283089eb4,求eqId16396ab536cf462399ed2cefb9763997的面积.
单选题 | 一般(0.65) | 2021·全国(理)
6 . 已知eqId052844cae8574a8ab842c38a039baac0是锐角△eqIda670baf5d73f4d7689915a00c51820f2的一个内角,若eqId373397dbaa3042598e6ac03a208286a4,则eqIdd2ef6663f7e7479fb5379305dd7377fe(   )
A.eqIdda3fe57e250a4b619aa9e3418e1534a4B.eqIdea67abfe0c564a4da4a636a0f83f7aca
C.eqId49b7b111d23b44a9990c2312dc3b7ed9D.eqIde4d58f42bad9461b93d451da718fc6f4
7 . 在△ABC中,角ABC的对边分别为abc,其中b=3,且满足eqId74303b82eb1d46bd92b6c939e9f59536.
(1)求角B的大小;
(2)若a+c=5,求△ABC的面积.
8 . 在△eqIda670baf5d73f4d7689915a00c51820f2中,内角eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3的对边分别为eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqId44925af6fb19413689ba5616e3647cba,且eqId56a28c1de0ec47b692295c140ae54073,则角eqId052844cae8574a8ab842c38a039baac0的大小为________
9 . 在eqId64b9b599fdb6481e9f8d9a94c102300b中,内角eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3的对边分别为eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqId44925af6fb19413689ba5616e3647cba,已知eqIdd55149ef09f444c98bcef2788d37a37f.
(1)求eqId90be7156e574417bb57ec23a94e35503的值;
(2)若eqId943b1518b6924ae68f80e440b5b1ee65eqId25b656c733474b958f42ad2e43ff7c43,求eqId64b9b599fdb6481e9f8d9a94c102300b的面积.
10 . 在eqId64b9b599fdb6481e9f8d9a94c102300b中,角AeqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3所对的边分別为eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqId44925af6fb19413689ba5616e3647cba,且eqId96329b4e88e642f2942e9064b3be7aa6
(1)若eqIdda43591caa9542f780355a1d58dae3c1,求eqId64b9b599fdb6481e9f8d9a94c102300b的面积S
(2)若eqId312ef2c826304089b9b0f1d1e88b0f50eqIdcf2da96900c948a1b3ce7cbfd420c080的中点,且eqId1ba4d96170e241ba89e920f0d09081f0eqId2d255806f21242928d91b3d1ac9ff5fa,求eqId64b9b599fdb6481e9f8d9a94c102300b的最短边的边长.