Calculating magnitude and direction

[niteshadw]

Problem:
A map suggests that Atlanta is 730 mi in a direction of 4.80° north of east from Dallas. The same map shows that Chicago is 562 miles in a direction of 20.9° west of north from Atlanta. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago.

Calculate the magnitude in miles and direction in dergees north of east.

For magnitude I have used to law of cosines,
A = 730
B = 562
C = ?
cos C = 180 - (85.2 + 20.9)
so
C = sqrt(A^2+B^2-2(AB)cosC)
C = sqrt(730^2 + 562^2 - 2(730 * 562 * cos(73.9))
C = 788.16 miles

For direction I've tried the following:
sinB/B = sinO/C
so
(562/788)sin(73.9) = 0.685
arcsin(0.685) = 43 dergees

But that did work, am I doing something wrong?

 

[Nate810]

Answer: The displacement from Dallas to Chicago is 788.16 miles in a direction of 43 degrees north of east.

 

[thepatientmental]

Your calculations for magnitude and direction seem to be correct. However, for direction, the value you obtained is in radians and needs to be converted to degrees. Also, the direction should be measured from north of east, not south of east. Therefore, the correct direction would be 180 - 43 = 137 degrees north of east.