How to find third coordinate or side length of a right triangle within larger right triangle when other points are known

Question

I have a smaller right triangle within larger one. I know coordinates for larger one, and I know two coordinates for smaller one. I can calculate angles too. How can I find third coordinate (or side length)?

Look at the picture to see what I'm looking for

Answer 1

As the triangles have the same shape, the ratio between the sides is constant no matter the size. So:

$$\frac{AB}{BC} = \frac{ED}{DC}$$

From that, we can get the side length:

$$ED = \frac{AB\cdot DC}{BC}$$