Three towns A, B and C are connected by straight roads. B is due west of A, C is due south of B and the bearing of C from A is 220 degrees. If the distance from A to B is 300 km:

a) find the distance from A to C

b) find the bearing from A to C

Based on what you have given, the distance between A and C is 466.7 km, and the bearing from A to C is 220 deg. The bearing from C to A is the reciprocal, 40 deg.

(Edited)

Sorry, but the distance is not good.

The easiest way to do it is by having a sketch in front of you.

26502

You can find angle BAC by having 270 - 220 = 50 degrees
Using cos, you know that

cos 50 = \frac {300}{AC}

Solving for AC will give you 466.7 m.

Then, the bearing is indeed 40 degrees

I used the diagonal of a 300km x 300km square, and I was obviously wrong. OOPS. I mis-read something. Thanks. Unk!

It's OK, it might have happened to anybody including myself :)