Question

if the ratio of hree sides of a triange is a a:b:c =7:8:9 then show that cosa: cosb: cosc=14:11:6

Answer 1

let a=7x
b=8x and c=9x

cos a = b*b +c*c-a*a/2cb=64+81-49/2*72 =2/3
cos b = a*a +c*c-b*b/2ca = 81+49-64/2*63=11/21
cos c = a*a + b*b-c*c/2ab = 49+64-81/2*56=2/7

so ratio is 14:11:6