A plane is flying southeast at 215 km/h. Suddenly there is a wind from the north at 75 km/h. What is the plane's new velocity with respect to the ground in standard position?

Impose a coordinate system where positive x axis direction is east, positive y axis is north, negative x axis is west and negative y axis is south: plane's velocity is directed southeast (i.e. along the bisector of the IV quadrant), while wind blows from north to south: you have that the angle between these 2 velocity vectors is 45 degrees, so sum these vectors.