The point B is 280m due north of point A. A man walks from A in the direction 050(degrees). Calculate how far he has to walk before he is as close as possible to B

(b) as close as possible to B means that the line BD is perpendicular to the 050 bearing line and so AB is a hypotenuse

So use the basic cosine ratio:

cos 50 = BD/280

BD = 280 cos 50

BD = 179.98

So after walking for 180 m he is as close to B as he is going to get on the 050 bearing