A man walks due west for 4 km. He then changes direction and walks on a bearing of
197° until he is south-west of his starting point.
How far is he then from his starting point? with workings​

Step-by-step explanation:

Let the starting point be B and the stopping be C as shown in the diagram below.

therefore, the angle at A will be (197-90)degree = 107degree

the angle at B is 45degree, since it is directly south west of C.

therefore the angle at C will be A+B+C=180 degree(sum angle of a triangle)

107+45+C=180

therefore, C=180-107-45=28degree

therefore, using sine rule gives;

sinA/a =sinC/c

sin107/a=sin28/4

0.9563/a=0.4695/4

0.9563/a=0.11736

therefore, a =0.9563/0.11736=8.148=8.1km(approx.)