I’m trying to find the coordinates of an unknown point © in a right angled triangle. Allow me to attempt to demonstrate:
I need to find C given A, B, AB and BC
I know the points A and B and therefore know the length of the side connecting them (AB). I also know the length of BC and that there is a right angle at point C. Finding the length of AC using Pythagoras and the unknown angles using trigonometry is trivial. The problem is that I do not know how to find the coordinates of point C efficiently.
I already know I can test a circle centred on the midpoint of AB, diameter equal to that sides length, with a circle centred on B, radius equal to the length of BC. I’d prefer to avoid doing this though as it seems like an overkill, and I am hoping for the fastest method as this calculation will be a vital part of a path finding routine and will be called upon hundreds of times in one search (the true problem is finding a tangent to a circle that runs through a given point).
Thanks for any help,