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If in triangle ABC, b+c/11=c+a/12=a+b/13 prove that cosA:cosB:cosC=7:19:25.

If in triangle ABC, b+c/11=c+a/12=a+b/13 prove that cosA:cosB:cosC=7:19:25.

Grade:11

1 Answers

Arun
25763 Points
3 years ago

Let ,b+c/11=c+a/12=a+b/13 = k    b+c = 11k  c+a = 12k  a+b = 13k    Add a +b +c = 18k      a = 7k  b= 6k   c = 5k

cos A = (6k) + (5k) - (7k) )/2(6k)(5k)  = 1/5 = 7/35

cos B = (7k) + (5k) - (6k) )/2(7k)(5k)  = 19/35

cos C = (6k) + (7k) - (5k) )/2(6k)(7k)  = 5/7  = 25/35

cosA/7=cosB/19=cosC/25

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