2D geometry: how to check if a point is inside an angle

Question

i have the following geometrical issue in 2D:

i have a point from which i cast an infinite angle (2D-cone) which is given by a direction and an angle. (the point and th

Answer 1

I would say the best way is to project the point onto the 2D surface perpendicular to the cones direction. Then you calculate the othogonal distance between that same plane and the point. Finally, you know the width of the cone at that height, so you can see if the point is outside that width.