批踢踢實業坊 ask 板: Re: [請問] 請問一題角度－

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批踢踢實業坊 ask 板

Jun 22nd 2014, 14:33, by Schottky

作者Schottky (順風相送)

站內ask

標題Re: [請問] 請問一題角度

時間Sun Jun 22 14:33:44 2014

※ 引述《wjx0305 (胖包子~)》之銘言： : ABD、ACE都是正三角形，角DFB是幾度？ : http://doublefish12.pixnet.net/album/photo/283372383 用解析幾何: 令 A=(0,0), B=(-1,-√3), D=(-2,0), C=(x,(-√3)X), E=(2x,0) 如此正三角形ABD邊長為2, 正三角形ACE邊長為2x 以三角形DEF的觀點，外角DFB = 角EDF + 角DEF 設角EDF = α, 角DEF = β，題目要求的角 DEF = α+β tan α = ((√3)x)/(x+2) tan β = (√3)/(2x+1) 使用和角公式 tan (α+β) = (tan α+tan β)/(1-tan αtan β) 代入化簡以後會發現 x 被消光光，tan (α+β) = √3 所以 α+β= 60度 -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 220.137.26.153 ※ 文章網址: http://www.ptt.cc/bbs/ask/M.1403418826.A.73E.html

推 Aragorn:這是國中數學其實沒有這麼複雜啦~ 06/22 15:03

推 OAzenO:這題大概三角函數是唯一解法大大高手 06/22 15:12

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