Euler character of etale finite cover

Euler character of etale finite cover

Let $\pi: \tilde{X} \to X$ be an etale finite cover, then why the Euler
character has relation:
$$\chi(\tilde{X},\mathcal{O}_{\tilde{X}})=\deg(\pi)\chi({X},\mathcal{O}_{{X}}).$$
I try to use Riemann-Roch, but do not know how to relate Chern characters
and Todd class of them.
Besides, I found a similar question on topological setting.