a-maths~~~~~~

2007-10-16 4:24 am
在∆ABC中,A:B:C=1:2:3,求a:b:c。

回答 (2)

2007-10-16 5:12 am
✔ 最佳答案
A:B:C = 1:2:3
Let A = x, B = 2x and C = 3x.
x + 2x + 3x = 180° (三角形的內角和)
x = 30°
∴A = 30°, B = 60°, C = 90°
根據正弦定律,
a/sin 30° = b/sin 60° = c/sin 90°
a/(1/2) = b/[√(3)/2] = c/1
a/1 = b/√3 = c/2
∴a:b:c = 1 : √3 : 2
2007-10-16 4:39 am
1:sqrt(3): 2


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