Two men P and Q set out prospecting for oil from a base camp R. P moves 20km on a bearing of 205 degree and Q moves 30km on a bearing of 060. Calculate The distance from Q to P

Answer 1

determine the angle between the paths (205--60)=145
apply the law of Cosines:
c^2=a^2+b^2-2abCosC

Answer 2

All angles are measured CW from +y-axis.
d = 20km[205o] - 30km[60o].
X = 20*sin205 - 30*sin60 = -34.43 km.
Y = 20*Cos205 - 30*Cos60 = -33.13 km.
d = sqrt(X^2 + Y^2).