C _ _ _ _ _ _ B \ |_| \ | A = (ax,ay) \ | B = (bx,by) \ | BC = L \ | C = (?,?) \ | \ | \ | \ | \ | \| A
Okay so lets say you are given coordinates of points A, B and the length of BC. How do you find the coordinates of vertex C knowing it is a right triangle?
With the information I know I can get length AB(distance formula), length AC(Pythagorean), and then all the angles using law of sines but still at a blank on how to find C.
Edit: The sides are not necessarily parallel to or on any axis. The triangle may be rotated in any direction on the Cartesian plane.
Any guidance would be really helpful! I feel like this is a simple geometry problem and I have tried searching the internet but only find problems similar to this one and I can't figure it out.
Again any help would be really appreciated :) Thanks in advance!