# Finding length of some sides on a triangle construction.

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 $$AE=AC-EC$$