Math Pro 數學補給站's Archiver

A man becomes learned by asking questions.
人的學問,由好問而來。

bch0722b 發表於 2014-7-13 22:02

算算角度

如圖,在三角形ABC中,AB=AC,
延長AB到點D,延長CA到點E,使AE=BD,連接DE。
若DE=DA=BC,則角ABC的度數為多少?[img]http://140.112.17.195/attachments/forumid_8/1407131349976507e4b0f45b73.png[/img]

tsyr 發表於 2014-7-13 22:59

40度
應該不會錯

cefepime 發表於 2014-7-14 00:03

40 度。
加一票~

tsyr 發表於 2014-7-17 22:41

來個做法

作平行四邊形BDFC,DE = EC = AD
因為∠FCA =∠DAE =∠DEA,DE = EC,DE = CF
所以∆ADE全等於∆FEC,故CE = EF
注意DE = EC = AD = BC = DF = EF,∆DEF為正三角形
設∠ABC = X,則∠DAE = 2X,∠ADE = 180°-4X,∠ADF = X
∠ADF +∠ADE = 60°,即X =∠ABC = X = 40°

bch0722b 發表於 2014-7-18 16:52

我是做三角形BDF=ADE,你懂得...(F的位置)

cefepime 發表於 2014-7-18 21:27

[size=3]我的方法:[/size]
[size=3]
[/size]
[size=3]令∠ABC = θ[/size]
[size=3]
[/size]
[size=3]AC/sinθ = BC/sin(π-2θ) = DE/sin2θ = AE/sin(π-4θ)[/size]
[size=3]又 BC - AC = AE[/size]
[size=3]
[/size]
[size=3]故 sin2θ - sinθ = sin4θ[/size]
[size=3]
[/size]
[size=3]-sinθ = 2(cos3θ)(sinθ)[/size]
[size=3]
[/size]
[size=3]cos3θ = -1/2 (0<θ<45°)[/size]
[size=3]
[/size]
[size=3]3θ = 120°[/size]
[size=3]
[/size]
[size=3]θ = 40°[/size]

bch0722b 發表於 2014-7-18 21:32

哇,這方法好獨特~~三角函數用的徹底阿!!!厲害

頁: [1]

論壇程式使用 Discuz! Archiver 6.1.0  © 2001-2007 Comsenz Inc.