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

[Jerome1]

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

 

[Prove It]

Have you drawn a diagram yet?

 

[soroban]

Hello, Jerome!

An airplane flew from A to B on a bearing of 65^o for 60km.
It then flew from B to C on a bearing of S 25^o W for 86km.
Calculate (1) the bearing of C from A,
. . . . . . . (2) the distance between A and C.

                  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 $$AC.$$