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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?

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# Calculating magnitude and direction

Can you offer guidance or do you also need help?

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