I understand the calculation of a slope with the formula $$ \tan(slope) = \frac{\text{difference of elevation}}{\text{horizontal advancement}} = \frac{3}{5} = 0.6 $$
But a book about Geographic Information System tells me that it has some interest to calculate instead
$$
tan(slope) = \sqrt{b^2 + c^2}
$$
with
$b$ : difference of elevation by meter on the $x$ axis
$c$ : difference of elevation by meter on the $y$ axis
But this last formula, I am unable to understand it clearly and I fail on a digital application.
I can't reach 0.6 and I can't find the values of $b$ and $c$
If I am naive and attempt a
$tan(slope) = \sqrt{5^2 + 3^2}$
it leads to $\sqrt{36}$ = 6, not 0.6...
So I know that I'm doing wrong.
Can you help me? What are the values of $b$ and $c$?
What do they really depict? They are troubling me a lot.
The original text describing the formula I'm trying to understand:
