Vector problem, determining angle

[mickellowery]

Homework Statement

A plane travels from base camp to lake A, 280 km away in the direction 20⁰ north of east. After that it flies to lake B which is 190 km at 30.0⁰ west of north from lake A Graphically determine the distance and direction from lake B to the base camp.

Homework Equations

I used law of cosines to find the distance. R=$$\sqrt{}(280²+(190)²-2x280x190xcos(80)$$ I got 310km for the distance and this part is correct but its the angle that I'm not getting right.

The Attempt at a Solution

I tried the law of sines for this and its not turning out right. I tried 190/320xsin80 = .585 Then I did arctan .585 and got 30.3 which is wrong. It is supposed to be 57.2⁰ South of West

 

[thebigstar25]

I made a figure for this problem so you can see what you have to do:

http://img268.imageshack.us/img268/9506/24287615.jpg


I would suggest you use the law of cosine again to obtain angle (1) .. then obtain angle (2) .. from angle (2) you can easily obtain angle (3) which is the angle describing "the south of west" angle ..