I must find the length of $DE$ and $EC$
Pythagoras told me the length of $AB$, and I know that the right angles give me similar triangles, but I don't know how to proceed.
Also tried Pythagoras on the triangle $DEC$ but got nothing.
Some hint or help is very welcome !
As you mentioned Pythagoras gives us that $AB=15$, then use the similarity of triangles:
$\frac{DE}{DC}=\frac{AB}{AC} \rightarrow DE=\frac{15 \cdot 15}{20}=11.25$
Now, use Pythagoras to find $EC$ and then $AE=AC-EC$