A plane is flying in a storm. A GPS system

Question

measures the plane heading at an angle 23◦ west
of south, with a speed of 180 mph, relative to
the ground. A nearby weather station measures
the wind’s velocity to be 30◦ north of east, at a
speed of 50 mph.
Below, write a vector equation which gives
the plane’s velocity relative to the air (~vP/A)
in terms of its velocity relative to the ground
(~vP/G) and the air’s velocity relative to the
ground (~vA/G). Draw the corresponding vector
addition (or subtraction) to the right. What is
the magnitude and direction of the plane’s velocity

Answer 1

All angles are measured CW from +y-axis.
Vpa = 180[203o] + 50[60o].
Vpa = x+yi = (180*sin203+50*sin60) + (180*Cos203+50Cos60)i.
Vpa = -27 - 140.7i = 143mph[11o] W. 0f S. = 143mph[191o] CW.
TanA = x/y.