Asingle-engine airplane is heading due east at a constant speed of 150 mi / h. there is a 30 mi / h cross wind blowing north. what is the plane's actual speed and direction? round angles to the nearest degree and other values to the nearest tenth.

Let
F1 > airplane speed 150 mi / h East
F2 > wind  speed 30 mi / h North

calculate the resultant force R
F1x=150    F1y=0      F2x= 0  F2y=30
Rx=F1x+F2x >150+0 >Rx=150
Ry=F1y+F2y >0+30  >Rx=30
║R║=√150² 30²=√23400=152.97 >153 mi/h
tan(theta)=Ry/Rx=30/150=0.20
arctan (0.20)=11.31 degrees11.3 degrees

 the answer is
actual speed 153 mi/h and direction 11.3 degrees North-East  (I Quadrant)