Question

A person walks 38 m East and then walks 33 m at an angle 46° North of East. What is the magnitude of the total displacement? Answer in units of m.

Answer 1

This is direct application of the cosine theorem.
c^2=a^2+b^2 - 2*a*b*cos(Theta)

in our case:
a=38
b=33
c=?
Theta=180-46=134
cos(Theta)=cos(134)=-0.7
c^2=33^2+38^2+2*33*38*0.7
c^2= 1089+1444+1755.6
c^2=4288.6
c=sqrt(4288.6)=65.48=65.5m

ANSWER:
distance=65.5m