Finding the point which divides a triangle into 2 right triangles

Question

I have 3 points that define a non-right triangle - say A,B,C. How can I find the point D along an (any?) edge such that the angle formed by ABD and BCD (or similar) are 90°?

Answer 1

I suppose your triangle should look something like this and you are interested in $e$ or $d$.

If you know $b$ and $\gamma$, you can calculate $e$ with the help of the cosinus:

$b \cdot cos(\gamma) = e$ and hence you know the position of the point $D$ you meant.