Displacement from Dallas to Chicago

[physics=death]

Hello, I am having some trouble with this question:
A map suggests that Atlanta is 731 mi in a direction of 4.90° north of east from Dallas. The same map shows that Chicago is 561 miles in a direction of 21.1° west of north from Atlanta. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago.

Here's what I did:
731cos(4.90)= 728
731sin(4.90)= 62.4

728+62.4= 790.4

561cos21.1= 523
561sin21.1= 202

523+202= 725

790.4+725= 1515.4 miles<----- magnitude of displacement

I have no idea if I am doing it right...

[MajestikMoose]

Your best bet is to draw a triangle and fill it in with the information you have. You're given two of the lengths so all you need to do is find one of the internal angles and then apply the cosine rule.

Remember that on a flat Earth that there are 90 degrees between North and East, East and South and so on.

[Dick]

Displacement is a vector. You probably do want to use vectors. So you've got the Dallas-Atlanta vector to be (728,62.4)mi. The first component is EW distance (E positive) and the second is NS distance (N positive). On the second one you have a problem. The angle should be measured counterclockwise from east. You are given the angle from north. Can you fix that? Then how do you combine the two vectors to get Dallas-Chicago?