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.
[Math] Find 3rd side, given two sides and bearings
trigonometry
Best Answer
According to the US Army definition of bearing, which this question seems to be using by the format, the layout is as follows:
$\hspace{3.5cm}$
Using the Law of Cosines, we get $$ \begin{align} \overline{AC}^2 &=\overline{AB}^2+\overline{BC}^2-2\overline{AB}\,\overline{BC}\cos(\angle ABC)\\ &=65^2+130^2-2\cdot65\cdot130\cos(86^\circ) \end{align} $$