In triangleABC,a:b :c=3:7:9.

9>7>3
Cosw
=(3^2+7^2-9^2)/(2*3*7)
=(9+49－81)/42
=－23/42
w=123.2degree

Since a:b:c=3:7:9, and

Let a=3x, then b=7x and c=9x

By observing such a triangle, the largest angle must faces the longest side, therefore C is the largest angle.

Cosine rule:
a^2+b^2-2abcosC=c^2
9x^2+49x^2-42x^2cosC=81x^2
9+49-42cosC=81
-42cosC=81-49-9=23
cosC = -0.5476
C= 123.2 degree