Please help physics prob?

Question

On a training flight, a student pilot flies from Lincoln, Nebraska to Clarinda, Iowa, then to St. Joseph, Missouri, and then to Manhattan, Kansas (Intro 1 figure) . The directions are shown relative to north: 0 degrees is north, 90 degrees is east, 180degrees is south, and 270 degrees is west.

http://session.masteringphysics.com/problemAsset/1041176/3/yf_Figure_1_33.jpg

a) Use the method of components to find the distance she has to fly from Manhattan to get back to Lincoln.

b) Find the direction (relative to north) she must fly to get there.

Answer 1

if   X(lin)=0 & Y(lin)=0



then   X(cla)=147*sin(85)=146.44 km

          Y(cla)=147*cos(85)=12.82 km

&

        X(St)=106*sin(167) + 146.44 =170.28

        Y(St)=106*cos(167) + 12.82 =-90.46

&

       X(man)=166*sin(235) + 170.28 =34.30

       Y(man)=166*cos(235) +(-90.46)=-185.67

X(return to lincoln)=-34.30

& Y(return to lincoln)=+185.67

(a) total way =188.82 km

(b) arccotg theta = (185.67/-34.30) = -10.46