在锐角三角形ABC中，A=2B，B、C的对应边分别为b、c，则c/b 的取值范围！ 在锐角三角形ABC中A=2B,a.b.c.所对的角分别为A....
\u5728\u9510\u89d2\u4e09\u89d2\u5f62ABC\u4e2d,A=2B,B,C,\u6240\u5bf9\u7684\u8fb9\u957f\u5206\u522b\u4e3ab,c,\u6c42b/b+c\u7684\u53d6\u503c\u8303\u56f4A+B+C=180\u00b0
\u9510\u89d2\u4e09\u89d2\u5f62 0\u00b0<A,B,C<90\u00b0
3B+C=180\u00b0
C=180\u00b0-3B
0\u00b0<180\u00b0-3B<90\u00b0
30\u00b0<B<60\u00b0
\u53c8\u56e0\u4e3a 0\u00b0<A<90\u00b0
\u6240\u4ee5 30\u00b0<B<45\u00b0
\u6b63\u5f26\u5b9a\u7406 a/b=sinA/sinB=sinA/sin2A=1/(2cosB)
\u221a2/2<cosB<\u221a3/2
\u6240\u4ee5 2\u221a3/3<a/b<\u221a2
0＜A+B＜180°
0＜2B+B＜180°
0＜3B＜180°
0＜B＜60°
C=180°-A-B=180°-3B
根据正弦定理：
c/sinC=b/sinB
c/b=sinC/sinB=sin(180-3B)/sinB=sin3B/sinB=sin(2B+B)/sinB
=(sinBcos2B+cosBsin2B)/sinB
=(sinBcos2B+2sinBcosBcosB)/sinB
=cos2B+2cos^2B
=2cos^2B-1+2cos^2B
=4cos^2B-1
0＜B＜60°
1/2＜cosB＜1
0＜4cos^2B-1＜3
即：0 ＜ c/b ＜ 3
绛旓細璇曢鍒嗘瀽锛閿愯鈻矨BC涓紝瑙扐銆丅銆丆鎵瀵圭殑杈瑰垎鍒负a銆乥銆乧锛A=2B锛屸埓0锛2B锛 ,涓 锛3B锛溝锛庘埓 锛淏锛 锛屸埓 锛渃osB锛 锛 鐢辨寮﹀畾鐞嗗彲寰 = 銆傜偣璇勶細涓。棰橈紝鏈杈冧负鍏稿瀷锛岀患鍚堟т篃杈冨己銆傝В棰樼殑鍏抽敭鏄敞鎰忕‘瀹氳B鐨勮寖鍥淬
绛旓細姝ｅ鸡瀹氱悊 锛歛/sinA=b/sinB锛宎=sinA/sinB=sin2A/sinB=2cosB 閿愯涓夎褰 锛屸埓0掳锛溾垹A=2鈭燘锛90掳锛屸埓0掳锛溾垹B锛45掳 鍙0掳锛溾垹C=180掳-鈭燗-鈭燘=180掳-3鈭燘锛90掳锛屸埓30掳锛溾垹B锛60掳 缁煎悎锛30掳锛溾垹B锛45掳锛宑os30掳=鈭3/2锛宑os45掳=鈭2/2 cos伪鍦紙0掳锛90掳锛変负 鍑...
绛旓細鍥犱负鏄閿愯涓夎褰锛屾墍浠2B鈮90掳锛 0锛淏鈮45掳 鎵浠osB鈭堬紙1锛屾牴鍙2/2]锛屽嵆a/b灞炰簬锛2锛屾牴鍙2]
绛旓細0锛2B+B锛180掳 0锛3B锛180掳 0锛淏锛60掳 C=180掳-A-B=180掳-3B 鏍规嵁姝ｅ鸡瀹氱悊锛歝/sinC=b/sinB c/b=sinC/sinB=sin(180-3B)/sinB=sin3B/sinB=sin(2B+B)/sinB =(sinBcos2B+cosBsin2B)/sinB =(sinBcos2B+2sinBcosBcosB)/sinB =cos2B+2cos^2B =2cos^2B-1+2cos^2B =4cos^...
绛旓細a/b = sinA /sin B = sin2B/sinB = 2sinBcosB/sinB = 2cosB A=2B 閿愯涓夎褰 浠绘剰涓や釜瑙掍箣鍜屽簲璇ュぇ浜90掳锛屽皬浜180掳 90掳< A+B = 3B < 180掳 A = 2B 锛 90掳 30掳锛 B < 45掳 鈭2/2 < cosB < 鈭3/2 鈭2 < 2cosB < 鈭3 鈭2 < a/b< 鈭3 ...
绛旓細姹傛渶闀胯竟涓庢渶鐭竟鐨勫彇鍊艰寖鍥?杩欒兘鏈夊彇鍊艰寖鍥?鍙互鍙栨棤闄愬ぇ 鏈闀胯竟涓庢渶鐭竟鐨勬瘮鐨勫彇鍊艰寖鍥?鏄繖?閿愯涓夎褰 A=2B 鎵浠 0锛2B锛90 鎵浠 0锛淏锛45搴 A+2B=3B锛90搴 鎵浠 30锛淏锛45搴 鎵浠 60锛淎锛90搴 鎵浠 45锛淐锛90搴 鎵浠 b杈规渶灏 (1)鎵浠ユ渶闀胯竟涓庢渶鐭竟鐨勬瘮鐨勬渶澶ф槸C瑙掓棤闄...
绛旓細鏍规嵁涓夎褰杈硅鍘熺悊锛歛/sinA=b/sinB.鍒,a/b=sinA/sinB=sin2B/sinB=2cosB.鍥犱负鈭燗+鈭燘+鈭燙=180搴.鎵浠3鈭燘+鈭燙=180搴.骞朵笖瑕佷繚璇佽嚦灏戔垹C鏄ぇ浜庨浂鐨,鍒欒B锛60搴.鎵浠/b鐨勫彇鍊艰寖鍥存槸锛1.2锛.
绛旓細c^2=a^2+b^2-2ab*cosC 灏A=2B鍗矪=A/2甯﹀叆,寰 C^2=锛5/4-cosC锛塧^2 (a/c)^2=1/(5/4-cosC) 閿愯涓夎褰腑,0
绛旓細璁＄畻濡備笅锛氶鍏堣纭畾瑙払鐨勫彇鍊艰寖鍥达紝鍥犱负A=2B锛涓斾笁瑙掑舰涓閿愯涓夎褰紝鍒30锛溾垹B锛45锛岋紙鑻モ垹B灏忎簬30锛屽垯鈭燙灏嗕负閽濊锛涜嫢鈭燘澶т簬45锛屽垯鈭燗灏嗕负閽濊锛夌敱姝ｅ鸡瀹氱悊鐭ラ亾AB/CA=sinC锛弒inB=sin(蟺-3B)锛弒inB=sin3B锛弒inB,鑰宻in3B=3sinB-4sinB^3,浠ｅ叆鍖栫畝寰桝B/CA=2cos2B+1,鍥犱负30锛溾垹B锛...
绛旓細a/b = sinA/sinB = 2cosB 0<A+B<180 0<B<60 1 < a/b < 2
