# geometry

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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 -

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 -

Thank you a ton!!

• geometry -

No problem!

• geometry -

To find the actual bearings, find the angles A,B,C, using the law of cosines. For example,

BC2 = AB2 + AC2 - 2*AB*AC*cosA

9 = 64 + 81 - 144cosA
cosA = 136/144
A = 19ยบ

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