Answer
See below
Work Step by Step
We are given $A, b,c$. Use law of cosines to find $a$:
$$a^2=b^2+c^2-2bc\cos A\\a=\sqrt b^2+c^2-2bc\cos A\\a=\sqrt 7^2+9^2-2(7)(9)\cos 35^\circ\approx5.18$$
Use law of sines to find: $\frac{\sin B}{b}=\frac{\sin A}{a}\\\sin B=\frac{\sin A}{a}\times b\\\arcsin (\sin B)=\arcsin (\frac{\sin A}{a}b)\\B=\arcsin(\frac{\sin A}{a}. b)\\B=\arcsin(\frac{\sin 35^\circ}{5.18}. 7)\approx50.8^\circ$
Since the sum of the triangle is $180^\circ$, we obtain:
$$A+B+C=180^\circ\\C=180^\circ-A-B\\C=180^\circ -35^\circ - 50.8^\circ\\C\approx94.2 ^\circ$$
