Let $(M,g)$ be a Riemannian manifold. Let $S_g$ be the corresponding Sasaki metric on $TM$. For every $p\in M$, $V_p\in T_pM$, is it true and obvious that $0_p$ is the closest point of the zero section to $V_p$?

With some abuse of terminology a rephrase of the question would be: Is the height of a right triangle shorter than its hypotenuse?