Answer:
Ground speed: 230 miles per hour.
Course: 156° clockwise from due north.
Explanation:
The plane speed is 190 heading 155° clockwise due north, is east is the horizontal of the coordinate plane (positive x-axis), the angle from the x-axis is:
The 360° is to avoid using negative angles, and the -90° is because the angle given in the data is measured from the north. Now do the same with the speed of the wind current (40 miles per hour at 160° clockwise from due north):
To find the course and ground speed of the plane find the components in x and y for both speeds and add them up.
The ground speed is the magnitude of this new vector:
The course is the angle:
This value of is the angle between the negative y-axis and the speed vector (see the graph). For the angle clockwise due north add 180°.