MHB What is the bearing and distance between cities A and C?

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The airplane flew from city A to city B on a bearing of 65 degrees, covering a distance of 60 km, and then from city B to city C on a bearing of S 25 degrees W for 86 km. To find the bearing of city C from city A, the Law of Cosines is applied to calculate the distance AC and angle BAC. The angle at point B is determined to be 40 degrees. By adding 65 degrees to the calculated angle BAC, the final bearing from A to C can be established. The discussion emphasizes the importance of using trigonometric laws for accurate navigation calculations.
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An airplane flew from city A on a bearing of 65 degrees to city B, a distance of 60km away. It then flew from B on a bearing of S 25 degree west to city C at a distance of 86km. Calculate (1) the bearing of C from A (ii) The distance between A and C
 
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Have you drawn a diagram yet?
 
Hello, Jerome!

An airplane flew from A to B on a bearing of 65o for 60km.
It then flew from B to C on a bearing of S 25o W for 86km.
Calculate (1) the bearing of C from A,
. . . . . . . (2) the distance between A and C.
Code:
                  B
      :           *
      :         */:
      :    60 * / :
      :     *  /  :
      :65[SUP]o[/SUP]* 40[SUP]o[/SUP]/25[SUP]o[/SUP]:
      : *    /    :
    A *     / 86  :
        *  /
          *
          C
You know: AB = 60,\;BC = 86,\;\angle B = 40^o

Use the Law of Cosines to find side AC.

Then use the Law of Cosines to find \angle BAC.
Add 65^o to find the bearing of AC.
 
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