如图(1),将Rt△AOB放置在平面直角坐标系xOy中,∠A=90°,∠AOB=60°,OB= ,∠AOB的平分线OC交
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/18 21:32:06
如图(1),将Rt△AOB放置在平面直角坐标系xOy中,∠A=90°,∠AOB=60°,OB=![]() |
![]() |
求:(1)OC、BC的长; (2)设△CPQ的面积为S,求S与t的函数关系式; (3)当P在OC上、Q在ON上运动时,如图(2),设PQ与OA交于点M,当t为何值时,△OPM为等腰三角形?求出所有满足条件的t值。 |
(1)在
中,
∴
∵
平分
∴
∴在
中,令
∴
∴
∴
(舍)
∴
∵
∴
。
(2)当
时,
当
时,
。
(3)
,
,
①
时,如图
∴
∴
∴
∴
∴
。
②
时,如图
∴
∴
过P点作
于点D
∴
∴
∴
∵
∴
∵
∴
∴
。
③
时,此时
,而
∴
故舍
∴当
或
时,
为等腰三角形。
![](http://img.wesiedu.com/upload/c/fb/cfba4ce91d066e214c532391dc0da290.jpg)
![](http://img.wesiedu.com/upload/2/64/2642020dc00ddfdbbc099080e43b7291.jpg)
∴
![](http://img.wesiedu.com/upload/7/16/7167ab3176009dd31ece33cd28211542.jpg)
∵
![](http://img.wesiedu.com/upload/3/b0/3b03fb437f7ce84b66561aaf8d914797.jpg)
![](http://img.wesiedu.com/upload/9/d6/9d63486ef50d2feae74a5d5855590b43.jpg)
∴
![](http://img.wesiedu.com/upload/e/e4/ee4a4f59daea5faa9b74dc214ffbd7df.jpg)
∴在
![](http://img.wesiedu.com/upload/f/c5/fc5659245bd1d4bec0f4f4565c888cce.jpg)
![](http://img.wesiedu.com/upload/d/89/d89851d3e31c871162249b63a45af85c.jpg)
∴
![](http://img.wesiedu.com/upload/9/48/948dea5667619e9834883dfbee5b4f72.jpg)
∴
![](http://img.wesiedu.com/upload/3/3b/33b9c25e650f048215f1fc886a4424ab.jpg)
∴
![](http://img.wesiedu.com/upload/e/2b/e2b3647495db55c5fe7d1dd1c7c751e6.jpg)
∴
![](http://img.wesiedu.com/upload/1/ac/1ac91d4c667375c6753bd20835b7dc4d.jpg)
∵
![](http://img.wesiedu.com/upload/c/11/c11adb3192026149de2fbd3ec2403153.jpg)
∴
![](http://img.wesiedu.com/upload/0/6f/06fcb06d74f6f6d9205b2684393cb247.jpg)
(2)当
![](http://img.wesiedu.com/upload/f/03/f03a4a74c83c28313cc9fee0739df562.jpg)
![](http://img.wesiedu.com/upload/1/df/1df1c3e183fec9e54f0e32c45a360faa.jpg)
当
![](http://img.wesiedu.com/upload/c/80/c80c196abf8f219998858d984844fa9a.jpg)
![](http://img.wesiedu.com/upload/2/2b/22b3ab0c8caad613ce4b3a7e33366bdd.jpg)
(3)
![](http://img.wesiedu.com/upload/8/37/837b3d66df3195a8fd90d49f7298bd4c.jpg)
![](http://img.wesiedu.com/upload/f/ed/fed5a21e3fc2e209e4ed27244e1c5f35.jpg)
![](http://img.wesiedu.com/upload/1/06/10632309854227effbc57230c07e565d.jpg)
①
![](http://img.wesiedu.com/upload/8/05/805fdc0710052a39b0c60649848ef075.jpg)
∴
![](http://img.wesiedu.com/upload/1/d6/1d64d6f314f887826f59e26aa21605b6.jpg)
∴
![](http://img.wesiedu.com/upload/d/a4/da4489784fd118b662f1c92057d55e97.jpg)
∴
![](http://img.wesiedu.com/upload/b/d7/bd7805c7cc4d3f81ffdabb2d4538842b.jpg)
∴
![](http://img.wesiedu.com/upload/7/41/74116606b74ae34e8cc29ca91ac6a617.jpg)
∴
![](http://img.wesiedu.com/upload/5/b5/5b5d653713552c6e5f209ea9f2211526.jpg)
![](http://img.wesiedu.com/upload/0/e9/0e90bce19e31f0ba9c0eda930cfc6c5c.jpg)
②
![](http://img.wesiedu.com/upload/6/fe/6fe8aa6f0c50f4de3a733522ea61fafe.jpg)
∴
![](http://img.wesiedu.com/upload/e/3d/e3dca259088ee77188b73f7a9d4ff3d1.jpg)
∴
![](http://img.wesiedu.com/upload/1/fe/1feaa6722e7c1af8f293c9e0f139ac3b.jpg)
过P点作
![](http://img.wesiedu.com/upload/3/78/378d2b603e7d615a9f1eca090d1a92c2.jpg)
∴
![](http://img.wesiedu.com/upload/b/80/b80970c75cdea24dea0ddbe25208d5f7.jpg)
∴
![](http://img.wesiedu.com/upload/a/0a/a0ab02fbdc171eb80c153e5036d25fd3.jpg)
∴
![](http://img.wesiedu.com/upload/d/1d/d1d5f21fb068b050629058102e32e043.jpg)
∵
![](http://img.wesiedu.com/upload/1/e0/1e083232781788f694980901098f9755.jpg)
∴
![](http://img.wesiedu.com/upload/b/b3/bb362aab81f7cb974e117b8423e3dbe3.jpg)
∵
![](http://img.wesiedu.com/upload/f/cb/fcbc26ca05991667133a0fdece387033.jpg)
∴
![](http://img.wesiedu.com/upload/9/be/9be4d42d5115ea4d10304bb3312f1040.jpg)
∴
![](http://img.wesiedu.com/upload/7/d5/7d53c9d0ae232c2d52c6f625b4527e1d.jpg)
![](http://img.wesiedu.com/upload/2/e5/2e5521eccc0ceb3ddea0620274eae352.jpg)
③
![](http://img.wesiedu.com/upload/d/2b/d2b0a48461e96539b40d28a2d4da8e08.jpg)
![](http://img.wesiedu.com/upload/1/97/197e3761b485baf2c4cf41567c37b8bb.jpg)
![](http://img.wesiedu.com/upload/c/8f/c8fd25537a9f2aae1351ef4e88c010f7.jpg)
∴
![](http://img.wesiedu.com/upload/0/88/088159257069316e6cee8b5d91baaa4b.jpg)
故舍
∴当
![](http://img.wesiedu.com/upload/f/f2/ff2bcad946e6f918c041dc535a967761.jpg)
![](http://img.wesiedu.com/upload/7/7d/77d5e9f1149cc2aa8fbe6b2a88abbbc0.jpg)
![](http://img.wesiedu.com/upload/a/5b/a5b6e0968e1992b68209cdfcb4b5ede1.jpg)
如图(1),在Rt△AOB中,∠A=90°,AB=6,OB=43,∠AOB的平分线OC交AB于C,过O点作与OB垂直的直
(2009•孝感)如图,将放置于平面直角坐标系中的三角板AOB绕O点顺时针旋转90°得△A′OB′.已知∠AOB=30°
如图1,在平面直角坐标系中,等腰Rt△AOB的斜边OB在x轴上,直线y=3x-4经过等腰Rt△AOB的直角顶点A,交y轴
如图1,在平面直角坐标系中,等腰Rt△AOB的斜边OB在x轴上,直线y=3x-4经过等腰Rt△AOB的直角顶点A,交y轴
如图Rt△AOB中,∠AOB=90°,OA=3cm,OB=3√3cm 以O为原点、OB为X轴建立平面直角坐标系.设P是A
如图,在平面直角坐标系内,已知OA=OB=2,∠AOB=30°. (1)点A的坐标为( ,); (2)将△AOB绕点O顺
在平面直角坐标系xOy中,△AOB的位置如图所示,已知∠AOB=90°,∠A=60°,点A的坐标为(-√3,1)
如图,在平面直角坐标系中,△AOB是直角三角形,∠AOB=90°,斜边AB与y轴交于点C
如图,在平面直角坐标系中,△AOB是直角三角形,∠AOB=90°,斜边AB与y轴交于点C.
如图 在平面直角坐标系中,△AOB是直角三角形,∠AOB=90°,斜边AB与Y轴交于点C.
如图,在平面直角坐标系中△AOB是直角三角形,∠AOB=90°,斜边AB与y轴交与点C
已知一个直角三角形纸片oab,其中∠aob=90°,oa=2,ob=4.将该纸片放置在平面直角坐标系中(如图①).