Question

An airplane travels 174 km on a straight course at an angle of 22.5 degrees South of East, it changes its course by moving 100 km, South and lastly moving 180 km, 30 degrees, West of South. Determine the resultant displacement, angle and direction.

Answer 1

$x=174\cos22.5°-180\sin30°=70.755\ (km)$

$y=174\sin22.5°+100+180\cos30°=322.47\ (km)$

$s=\sqrt{70.755^2+322.47^2}=330.14\ (km)$

$\alpha=\tan^{-1}(322.47/70.755)=77.6°\ (South\ of \ East)$