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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.

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flyguy557
The first plane is located 800 miles west of the origin (reference point). the other plane is located mainly south of the origin, but also 30 degrees west (that is, southwest of the origin), 1200 miles from the origin. If you draw a sketch, you'll see a triangle with horizontal side 800, hypotenuse 1200, and with one angle 60 degrees. Can you use this info to find the vertical side of this triangle? That'll be the distance between the two planes.