20-21高一·全国·课后作业
1 . 在已知三角形的两边a,b和一边的对角A,求角B时,如果A为锐角,那么可能出现以下情况(如图):
![](https://img.xkw.com/dksih/QBM/2021/11/11/2849051998388224/2849773829849088/STEM/1ce797be7392417390b7a52112b125bf.png?resizew=622)
如果A为钝角,那么可能会出现哪几种情况?试画出草图加以说明.
![](https://img.xkw.com/dksih/QBM/2021/11/11/2849051998388224/2849773829849088/STEM/1ce797be7392417390b7a52112b125bf.png?resizew=622)
如果A为钝角,那么可能会出现哪几种情况?试画出草图加以说明.
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20-21高一·全国·课后作业
2 . 在
中,
,
,
,
,求证:
为正三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d68d8db8d1effaeaf41e4b3feca64c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7a852eed68ad01c8ab84cd2c4b1df6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0d48340c15fcd96565bf71f8f18503.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c623a50c79b51d9f81feb7562cd67a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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20-21高一·全国·课后作业
解题方法
3 . 在任意三角形中,作一边上的高,就可以将边角关系问题转化为解直角三角形问题.仿照这种方法,在
中,设
,
,
,证明三角形的面积公式
,并运用这一结论解决下面的问题:
(1)在
中,已知
,
,
,求
;
(2)在
中,已知
,
,
,求b和
;
(3)证明正弦定理.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e781a2489271bfd1597cba1bb6f5887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df81cda12d7601d58b1d9c7c180c4d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c884a45b56bc34d79273b067c1520b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5472cb034a2abe60eb4e667dc3e88be.png)
(1)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcdb7a488910743dc5c63afb394b87e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e061053d6ad50b54ee7330ddb203ea1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5cbff84327e964f912a54032e76ccc9.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d39e8c6fc9149d6290c493a65bdc53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e54a36173cd9b7b28e91619d715cb569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15aa03a938c7d11e862ddd0579077c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5cbff84327e964f912a54032e76ccc9.png)
(3)证明正弦定理.
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4 . 如图,一艘船以42nmile/h的速度向正北方向航行,从
处看灯塔
位于船北偏东25°的方向上,30min后船航行到
处,从
处看灯塔
位于船北偏东58°的方向上.求灯塔
与
之间的距离(精确到0.1nmile).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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20-21高一·全国·课后作业
5 . 根据下列条件解三角形:
(1)
,
,
;
(2)
,
,
;
(3)
,
,
;
(4)
,
,
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b86d43790babcdbbdc03493ee70928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4982f5d53bf7abd67ef9f3e68ece36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413f9851aad373d782ae62b308f1de85.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/486160ebd73a249a96d369f8249cf114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c85ea29310d91178c68c1fd93d01d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59e29b822cda1ba926e96368094fa1a7.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0675b7f26277ed25496cb7269990739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f38fcb2207d0a78403c4af34653c2fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f4b7f2e28f1d0470ec9888172be4bb.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8db2ddebbe1b2afa140c825363a8f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30ebb2603c1da90c22e0abdd5131b0be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed5aef34b68655ef5d9891a6c1f8953.png)
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20-21高一·全国·课后作业
解题方法
6 . 在
中,
(1)已知
,
,
,求这个三角形的最长边的长;
(2)已知
,
,
,求a,c,B;
(3)已知
,
,
,求c;
(4)已知
,求B.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560cee14327be7db916ba73e4055710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba7f167e6b7932179cd855ef89effc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e8e720ab4c4a011132a4b1d6e09e18e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4612f3047394e85cfe05a7ead391e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdf129ac51b2901533ea2ade1457ef9d.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08ce80e91fdf435a8e3ec05be990e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3261f86e57147e353f7b5b5cca279c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09947ea5c9ea0fe010027f2aa91138b7.png)
(4)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a642521975821a57e50ae802ef41842.png)
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20-21高一·全国·课后作业
解题方法
7 . 根据下列条件,判断
的形状:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c747944478053389224dffa40c6ba8b7.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e02e6946143207c276f7430942c1b7.png)
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20-21高一·全国·课后作业
8 . 在一座
m高的观测台顶测得对面一水塔塔顶的仰角为
,塔底的俯角为
,求水塔的高度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
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9 . 为了在一条河上建一座桥,施工前在河两岸打上两个桥位桩A,B(如图).要测算出A,B两点间的距离,测量人员在岸边定出基线BC,测得
,
,
,试计算AB的长(精确到0.01m).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b3efec56dbdbf34de24bafa48d833a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc729f11518948ac1e05de0ca032b77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c774e94ae2da06ec6dc7490028ca915.png)
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20-21高一·全国·课后作业
10 . 判断下列结论是否正确,若不正确,试举例说明;若正确,请说明理由.
(1)若
,
,且
,则
;
(2)若
,
是三角形的两个内角,且
,则
.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a4a10e6ebab13cba83dec9d6662fba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca51be437b1a97ca92aa1159ab71102c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19dc38d888741a1b2e95fe0773a48c38.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca51be437b1a97ca92aa1159ab71102c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19dc38d888741a1b2e95fe0773a48c38.png)
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