An airplane is at a location 800 miles west of city x. another airplane is at a distance of 1,200 miles in a direction s 30° w from city x. what is the distance between the two airplanes to the nearest mile? assume that the planes are flying at the same altitude.

We can translate the given statements into 800 < 180 and 1200 <210. We are asked in the problem to determine the distnace between them, that is the resultant force of the two vectors. We add usng a calculator in the complex mode, that is equal to 1934.62 < -161.93. Amswer is 1934 miles

Law of cosines:
c^2 = a^2+b^2-2abcos C

c^2=800^+1200^2-2(800)(1200)cos 30

=417231.22

c = sqrt (417231.22) = 645.93 

answer is therefore: 646 miles.

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