Posted by **tori** on Thursday, February 16, 2012 at 10:54pm.

On a map, Town A is 8 km due south of Town B, Town C is 9 km from Town A, and Town C is 3 km from Town B (see figure below). Find the bearing from Town A to Town C and the bearing from Town B to Town C.

- geometry -
**yoyoma**, Thursday, February 16, 2012 at 11:33pm
Hello, there is no figure but I shall try my best to figure it out.

I think this is probably a triangle.

B

| C

| /

| /

A

AB= 8

AC=9

BC=3

A is 9 km SW of C and B is 3 km NW of C. I hope this helps.

- geometry -
**tori**, Thursday, February 16, 2012 at 11:48pm
Thank you a ton!!

- geometry -
**yoyoma**, Thursday, February 16, 2012 at 11:51pm
No problem!

- geometry -
**Steve**, Friday, February 17, 2012 at 10:47am
To find the actual bearings, find the angles A,B,C, using the law of cosines. For example,

BC^{2} = AB^{2} + AC^{2} - 2*AB*AC*cosA

9 = 64 + 81 - 144cosA

cosA = 136/144

A = 19º

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