Proof that I can always get a height function that is Morse.

Question

So a height function $h(x_{1},...,x_{m})=x_{k}$ for mfld $M^{m}\subset \mathbb{R}^m$.

I proved that Morse functions are dense in $C^{\infty}(M,\mathbb{R})$. So I can approximate h by Morse functions, but how can I make sure that there is a height morse function.

Please try to give me answers based on what I proved.