Find the distance between the cities. Assume that Earth is a sphere of radius 4000 miles and that the cities are on the same longitude (one city is due north of the other). (Round your answer to one decimal place.)
City Latitude
Dallas, Texas 32° 47' 39'' N
Omaha, Nebraska 41° 15' 50'' N

Question

Find the distance between the cities. Assume that Earth is a sphere of radius 4000 miles and that the cities are on the same longitude (one city is due north of the other). (Round your answer to one decimal place.)
City	    	Latitude
Dallas, Texas		 32° 47' 39'' N
Omaha, Nebraska		 41° 15' 50'' N

aaronq · Answer

i'm not familiar with these coordinates, but it's essentially finding the arc length.

|dw:1405647852125:dw|

Since they're on the same longitude (east-west), we consider them to be on the same plane.

so  arc length=$\large s=\theta *r=(\theta _1-\theta _2)*r$

you need to convert the degrees given to radians first though

e.g.  $\large 32^o*\color{red}{\dfrac{\pi}{180^o}}=0.56~ rad$

anonymous · Answer

Thanks.. Can you also tell me how to deal with angles given in this 32° 47' 39'' form.

aaronq · Answer

No problem. I'm assuming that for this question the latter part (47' 39'') doesn't matter because they are on the same latitude. I've also never used geographical coordinate systems so i have no idea. If you're interested take a look at this http://downloads2.esri.com/ESRIpress/images/205/121250-MapUse-samplechapter.pdf

anonymous · Answer

Thanks aloott. You're a lifesaver dude :D

aaronq · Answer

no problem man!