Map - climb

On the map of High Tatras in scale 1:11000 are cable car stations in the Tatranska Lomnica and in the Skalnate Pleso with distance 354.6 mm. Altitude of this stations are 949 m and 1760 m.

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

Result

α =  11.75 °

Solution:

\Delta h = 1760 - 949 = 811 \ m \ \\ \Delta x = 354.6 \cdot 11000 / 1000 = 3900.6 \ m \ \\ \ \\ \tan \alpha = \dfrac{ \Delta h }{\Delta x} \ \\ \ \\ \alpha = \arctan \dfrac{ \Delta h }{\Delta x} = \arctan \dfrac{ 811 }{ 3900.6 } \ \\ \alpha = 11.75 \text{ ^\circ } = 11^\circ 44'43" \ \\

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