Question

A person walks 30m due north, then 50m at 35 degrees. Find their total displacement.

Answer 1

Using the cosine rule (a^2 = b^2 + c^2 - 2bc cos A), we can work out the displacement:
Displacement = a
b = 30
c = 50
A = 180 - 35 = 145 degrees.

a^2= 900 + 2500 -1500*-0.81915...
      = 3400 + 1228.728...
      = 4628.72...
a = 68.034...
   = 68.0m (to 3s.f.).

To work out the angle from starting place, use another configuration of the cosine rule: 
$cos(C)= \frac{a^{2} +b^{2}- c^{2} }{2ab}$:
cos (C)= $\frac{4628.72...+900-2500}{2*68*30}$
           = 3028.7.../4080
           = 0.7423...
C = 42.069... degrees
   = 042 bearing