Map - climb

On the map of the High Tatras, on a scale of 1:11000, are cable car stations in the Tatranska Lomnica and the Skalnate Pleso with a distance of 354.6 mm. The altitude of these stations is 949 m and 1760 m.

What is the average angle of climb on this cable car track?

Correct answer:

α =  11.75 °

Step-by-step explanation:

$$\begin{gathered} \Delta h=1760-949=811m \\ \Delta x=354.6\cdot 11000/1000=3900.6m \\ \tan \alpha =\frac{\Delta h}{\Delta x} \\ \alpha =\arctan \frac{\Delta h}{\Delta x}=\arctan \frac{811}{3900.6} \\ \alpha =11.75^{\circ }=11°44^{\prime }43" \end{gathered}$$

Try another example