A Maths

(a+b) : (b+c) : (c+a) = 5 : 6 : 7
Let
a+b=5k...(1)
b+c=6k...(2)
c+a=7k...(3)
Combine:7k-a+5k-a=6k=>a=3k,b=2k,c=4k
Using consine rule
Cos A=[(b^2+c^2)-a^2]/2bc=(4+16-9)/16=11/16
Cos B=[(a^2+c^2)-a^2]/2ac=(9+16-4)/24=21/24
Cos C=[(b^2+a^2)-c^2]/2bc=(4+9-16)/12=-3/12
A=46.57,B=29,C=104.48

2009-01-29 18:21:58 補充：
EMK﹐我們的答案太似啦

2009-01-29 18:23:19 補充：
我忘記了correct to the nearest 0.1 degree
A=46.6,B=29.0,C=104.5

Let a+b=5k, b+c=6k, c+a=7k
then a+b+c=(5k+6k+7k)/2=9k
and thus a=3k, b=2k, c=4k.

By Cosine Law, we have
cosA = [b^2+c^2-a^2]/2bc = [2^2+4^2-3^2]/(2*2*4) = 11/16
Similarly,
cosB = [3^2+4^2-2^2]/(2*3*4) = 7/8
cosC = [3^2+2^2-4^2]/(2*3*2) = -1/4

Hence,
A = 46.6 degree
B = 29.0 degree
C = 104.5 degree