#### Answer

$a). less\, than \,13\, miles. $
$b). 6.058\, miles$

#### Work Step by Step

a). The distance travelled due North is less than 13 miles. Because the angle created is $25^{\circ}$. Had it been more than $45^{\circ}$ then it would have been more than 13 miles. And at 45 degrees it would have been equal to 13 miles.
b).If d is the distance travelled due N, then
$\frac{d}{13}= tan25^{\circ}=0.466$
$d=13\times 0.466=6.058\,miles.$