Question

A plane flies from base camp to lake a, a distance of 290 km at a direction of 20.0° north of east. after dropping off supplies, the plane flies to lake b, which is 170 km and 30.0° west of north from lake
a. graphically determine the distance and direction from lake b to the base camp.

Answer 1

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 = $\sqrt{a^2 + b^2}$

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