Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B.

Correct result:

h =  91 m

#### Solution:

$s=13 \ km \rightarrow m=13 \cdot \ 1000 \ m=13000 \ m \ \\ q=7/1000=\dfrac{ 7 }{ 1000 }=0.007 \ \\ \ \\ A=\dfrac{ 180^\circ }{ \pi } \cdot \arctan(q)=\dfrac{ 180^\circ }{ \pi } \cdot \arctan(0.007) \doteq 0.4011 \ ^\circ \ \\ \ \\ h=s \cdot \ \sin A ^\circ =s \cdot \ \sin 0.40106390596671^\circ \ =13000 \cdot \ \sin 0.40106390596671^\circ \ =13000 \cdot \ 0.007=90.99777=91 \ \text{m} \ \\ \ \\ h_{1}=13 \cdot \ 7=91 \ \text{m} \ \\ \ \\ h_{1} \approx h$

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