Two airplanes leave the airport at the same time. One plane is flying 700mph at a bearing of N46°W and the other plane is flying 895mph at a bearing of N43° E. After 3 hours, how far are the planes from one another?

9514 1404 393

  3380 miles

Step-by-step explanation:

The distance separating the planes can be found using the law of cosines. One plane has gone 3×700 = 2100 miles; the other has gone 3×895 = 2685 miles. The angle between their flight paths is 46°+43° = 89°. Then the separation (s) is ...

  s² = 2100² +2685² -2(2100)(2685)cos(89°) = 11,619,225 -11,277,000×0.01745

  s² ≈ 11,422,414.21

  s ≈ √11,422,414.21 ≈ 3379.7

The planes are separated by about 3380 miles after 3 hours.

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