We can simply find components of the given directions and conveniently add them up to find the total distance.
290 km 20 deg north of east can be decomposed as :
290 x cos(20) EAST + 290 sin(20) NORTH
=272.5 E + 99.18 N
Now from this point ,
170 Km 30 deg west of north :
170 cos(30) N - 170 sin (30) E [ east = - west]
= 147.22 N - 85 E
hence coordinates of lake b are
(272.5 - 85) E + (99.18 + 147.22)N
187.5 E +264.4 N
use right triangle property to find distance D = [tex]\sqrt{a^2 + b^2}[/tex]
D = 324.13 Km
and angle = atan(b/a) = 54.65 deg
hence lake b is at 324.13 Km 54.65 deg east of north
