在锐角三角形ABC中，已知A=2B，则a/b取值范围 锐角三角形ABC中,若A=2B,则a/b的取值范围是
\u5728\u9510\u89d2\u4e09\u89d2\u5f62ABC\u4e2d\uff0c\u82e5A=2B\uff0c\u5219a/b\u7684\u53d6\u503c\u8303\u56f4\u662f\uff1fa/b = sinA /sin B = sin2B/sinB = 2sinBcosB/sinB = 2cosB
A=2B
\u9510\u89d2\u4e09\u89d2\u5f62 \u4efb\u610f\u4e24\u4e2a\u89d2\u4e4b\u548c\u5e94\u8be5\u5927\u4e8e90\u00b0\uff0c\u5c0f\u4e8e180\u00b0
90\u00b0< A+B = 3B < 180\u00b0
A = 2B \uff1c 90\u00b0
30\u00b0\uff1c B < 45\u00b0
\u221a2/2 < cosB < \u221a3/2
\u221a2 < 2cosB < \u221a3
\u221a2 < a/b< \u221a3
\u6b63\u5f26\u5b9a\u7406
a/b
=sinA/sinB
=sin2B/sinB
=2sinBcosB/sinB
=2cosB
\u2235\u9510\u89d2\u4e09\u89d2\u5f62ABC\u4e2d
0<A<\u03c0/2
\u22340<2B<\u03c0/2
0<B<\u03c0/4
\u221a2/2<cosB<1
\u2234\u221a2<2cosB<2
\u2234\u221a2<a/b<2
\u9009C
\u5982\u679c\u4f60\u8ba4\u53ef\u6211\u7684\u56de\u7b54\uff0c\u8bf7\u70b9\u51fb\u5de6\u4e0b\u89d2\u7684\u201c\u91c7\u7eb3\u4e3a\u6ee1\u610f\u7b54\u6848\u201d\uff0c\u795d\u5b66\u4e60\u8fdb\u6b65\uff01
A=2B
锐角三角形 任意两个角之和应该大于90°，小于180°
90°< A+B = 3B < 180°
A = 2B ＜ 90°
30°＜ B < 45°
√2/2 < cosB < √3/2
√2 < 2cosB < √3
√2 < a/b< √3
a/b = sin2B/sinB = 2sinBcosB/sinB = 2cosB
锐角三角形ABC
30°< B < 45°
√2<a/b <√3
a/b = sin2B/sinB == 2sinBcosB/sinB = 2cosB
A=2B
0< B < 90°
0<A <180°
0 < cosB < 1
0 < 2cosB < 2
0 < a/b< 2
绛旓細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
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