A map suggests that Atlanta is 730 miles in a direction of 5.00 north of east fr

Question

A map suggests that Atlanta is 730 miles in a direction of 5.00 north of east from Dallas. The same map shows that Chicago is 560 miles in a direction of 21.0 west of north from Atlanta. The figure below shows the locations of these three cities. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago.

A map suggests that Atlanta is 730 miles in a direction of 5.00 north of east from Dallas. The same map shows that Chicago is 560 miles in a direction of 21.0½ west of north from Atlanta. The figure below shows the locations of these three cities. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago.

Explanation / Answer

XCOMPONENT OF FIRST VECTOR=730 cos 50

                                                               =727.2miles

X component of the second vector= -560 cos690

                                                    =-200.68miles

Adding net X component =526.51miles
similarly

YCOMPONENT OF FIRST VECTOR=730 sin 50

                                                              =63.62miles

Y component of the second vector= 560 sin69=522.8miles

Adding net Y component =586.42miles

Now the net displacement from Dallas to Chicago=526.512+586.422=788.10miles

direction tan?=586.42/526.51

                      =1.113

so angle ?=tan-1(1.113)

               =48.08degree

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