Answer
a. $1282.2\ miles$
b. $S\ 73.5^\circ \ E$
Work Step by Step
a. Draw a diagram as shown in the figure. As NA is parallel to BD, we have $\angle ABD=58^\circ$ and $\angle ABC=58+32=90^\circ$. In the right triangle ABC, we have $AC=\sqrt {(850)^2+(960)^2}\approx1282.2\ miles$
b. In the right triangle ABC, let $\theta=\angle BAC$, we have $tan\theta=\frac{960}{850}$, and we can find $\theta\approx48.5^\circ$. Thus the bearing from A to C is $S\ (180-58-48.5)^\circ \ E$ or $S\ 73.5^\circ \ E$
