Find 3rd side, given two sides and bearings The bearing from A to B is N $42^\circ$ E. The bearing from B to C is S $44^\circ$ E. A small plane traveling $65$ miles per hour, takes $1$ hour to go from A to B and $2$ hours to go from B to C. Find the distance from A to C.

Start at $A$, go $42^o$ to B and then head $46^o$ to $C$. So the angle at $B$ is $(90-42)^o+46^o=94^o$,  $c=AB=65$ and $a=BC=130$.  Now use the law of cosines
$b^2=a^2+c^2-2ac\cos B$ to get $b=149.34$
