Question

If an airplane travels 48.0° north of east for 251 km, how far east and how far north did it travel? In other words, what are the magnitudes of the east component and north component of the plane's displacement?

Answer 1

Displacement of airplane is $d=251\,km$ ,at an angle of  $\theta=48.0\degree$ north of east.

Magnitude of displacement along east is $d_{E}=251\cos 48.0\degree=167.95\approx 168.0\,km$

Airplane has traveled $168.0\,km$ along east.

Magnitude of displacement along north is $d_{N}=251\sin 48.0\degree=186.53\approx 186.5\,km$

Airplane has traveled $186.5\,km$ along north.