作者Honor1984 (奈何上天造化弄人？)
看板Math
標題Re: [中學]求幫助
時間Fri May 12 22:47:43 2023
※ 引述《sienna0913 (玉荷包)》之銘言：
: 表弟來玩 求我幫他但是我也離開學校很久
: 可以求個各位的幫助嗎 解法跟答案
: https://i.imgur.com/l5hJHsn.jpg
: https://i.imgur.com/FDxd37K.jpg
5/sinx = 5k/sin(ADB) = AD/sin(60度)
7/sinx = 7k/sin(ADB) = AD/sin(ACB)
(1)
5k/sin(ACB) = 7k/sin(60度)
=> sin(ACB) = (5/7)(sqrt(3))/2 = (5/14)sqrt(3)
(2)
由(3)知k = 3/2
=> 12/sin(BAC) = 7(3/2)/sin(60度)
=> sin(BAC) = (8/7)(1/2)sqrt(3) = (4/7)sqrt(3)
(3)
144 + 25k^2 - 60k = 49k^2
=> 2k^2 + 5k - 12 = 0 => k = 3/2
=> AB = 5k = 15/2
: https://i.imgur.com/beCee03.jpg
沒有問題，就是正弦定理
: https://i.imgur.com/TjfX2EO.jpg
AD/sin(45度) = 6/sin(30度)
=> AD = 12/sqrt(2) = 6sqrt(2)
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