Question

A man start from point A and walks 5km east to B. He then walks 7km on a bearing of 162 degree to reach point C. Find the bearing and distance of C from A

Answer 1

make your sketch, to see a triangle with sides 5 and 7 and the contained angle of 108°
by the cosine law:

AC^2 = 5^2 + 7^2 - 2(5)(7)cos108
= 95.6311...
AC = √95.6311.. = 9.778... (I stored that in memory)

by sine law:
sinØ/7 = sin108/9.778..
sinØ = .68077...
Ø = appr 42.9° -----> E 42.9° S

or, using vectors:

R = (5cos0 , 5sin0) + (7cos -72, 7sin -72)
= (5, 0) + (2.16312 , -6.6273..)
= (7.163... , -6.6273..)

|R| = √(7.163..^2 + (-6.6273..)^2)
= 9.779 , same as above

tanØ = -6.6273../7.163...
Ø = -42.9° ----> E 42.9° S , same as above