A boy walks 4 km due west. He then changes direction and walks on a bearing of 214∘ until he is south-west of his starting point. How far is he from his starting point? Correct your answer to one decimal place.
Worked solution (try it first)
Put the start at the origin.
After the first leg he is at (−4,0).
On 214∘ (that is, 34∘ west of south), walking t km adds (−tsin34∘,−tcos34∘).
South-west of the start means as far south as west: 4+0.5592t=0.8290t, so t≈14.83 km.
He is then about 12.29 km west and 12.29 km south, so his distance is 12.292≈17.4 km, option E.