Height difference

What height difference is overcome if we pass a road 1 km long with a pitch21 per mille?

Correct answer:

x =  20.9954 m

Step-by-step explanation:

$$\begin{gathered} \tan \alpha =21\mathrm{/}1000 \\ \alpha =\arctan 21\mathrm{/}1000=0\mathrm{°}{1}^{\mathrm{\prime }}16\mathrm{"} \\ x=1000\sin \alpha =20.9954\text{ m} \end{gathered}$$

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