Question

A girl walks 800km on a bearing of 129 degree. Calculate how far east and south she is from her starting point.

Answer 1

A "bearing of 129°) is the same as -39° in normal trig notation.

Make a sketch in the x-y plane, the origin being her starting point
From this right-angled triangle:
sin(-39) = y/800
y =800sin(-39) = -503.5 km <---- south of her starting point
cos(-39) = x/800
x = 800cos(-39) = 621.7 km <---- east of her starting point

walking 800 km?? rather absurd question. Metres instead of km
would make more sense.