Hi there! Thank you for the opportunity to help you with your question!
This question can be better answered by doing vector additon. The airplane is moving 30 degrees south of west (that is, if you have the West-East axis be your x-axis, and the South-North be your y-axis, then the plane will make an angle of 30 degrees with the x-axis.) We then draw a vector with magnitude 160m/s in that direction, that is the airplane with respect to the air. Now, we must add the vector due north with magnitude 41m/s.
The x-coordinate is given by -160*cos(30 degrees) + 0 = -160sqrt(3)/2
the y-coordinate is given by -160*sin(30 degrees) + 41 = -39
And now the heading is given by the arctan of the two components. theta = arctan[39/(160*sqrt(3)/2)] = 15.72 degrees (south of due west), or 180+(90-15.72) = 254.28 degrees.
Please let me know if you need any clarification. Always glad to help!
Content will be erased after question is completed.