Hello, VictorL!

Is there enough information to answer the following question?

Two hikers are in the field out of each other's sight.

They each have a cell phone and a compass.

They want to meet together someplace along the straight line that connects their current positions.

They call each other and agree on a distant landmark visible to each.

They report to each other their bearing (degrees from North) to the landmark.

Can they now decide the proper bearing to walk to meet up in the shortest distance?

I say "No" . . . There is insufficient information.

Suppose the landmark is "between" the two hikers, $\displaystyle A$ and $\displaystyle B.$

A diagram might look like this:

Code:

L
o
* * :
* * :
: * * :
: * * β :
:α * * :
: * o B
:* *
A o *
* *
* *
* *
* K M *

The landmark is at $\displaystyle L.$

The hikers are at $\displaystyle A$ and $\displaystyle B.$

$\displaystyle A$'s heading to the landmark is $\displaystyle N \alpha^oE$

$\displaystyle B$'s heading to the landmark is $\displaystyle N \beta^o W$

But $\displaystyle A$ can be *anywhere* on the line $\displaystyle LK.$

And $\displaystyle B$ can be *anywhere* on the line $\displaystyle LM.$

There is not enough information for their meeting.