Considering a cartesian plane; There is a line from point A to B, at any angle from the horizontal axis. We need to draw another line from point B to C. The distance d of the new line is given as well as the angle a it will have from the first line. We need to find the x and y coordinates of the point C.
Explanation:
Lets suppose I have point A on the cartesian plane as such { Ax : 10 , Ay : 10 }. I have another point B such that { Bx : 20 , By : 20}. Now I need to find a point C in terms of Cx and Cy. While I have the length of the line BC or the magnitude of the vector BC; that is d = 20. And also the Angle AC that is a = 135. The Image attached also clarifies it further.
I found a solution to draw a line at 90 degrees from the end of a line, but it doesnt gives a solution for other angles. I also found a solution to find a point from a particular point at an angle relative to the X-axis, but it doesnt gives a solution for the angle being relative to a line instead.
Image Attached
Best Answer
Following an anticlockwise angular convention.
Let angle between AB and BC be $\beta $ and let the slope of AB be $\phi$
$$ xC= xB + d \cos ( \pi + \phi -\beta) $$
$$ yC= yB + d \sin ( \pi + \phi -\beta) $$