#### Answer

(a) The pilot must fly 54.2 miles at an angle of $26.4^{\circ}$ north of east.
(b) The pilot must fly an extra distance of 134.2 miles.

#### Work Step by Step

(a) We can find the total west component of the two extra parts of the flight:
$55~mi - (25~mi)~sin~15^{\circ} = 48.5~mi$
We can find the total south component of the two extra parts of the flight:
$0 +(25~mi)~cos~15^{\circ} = 24.1~mi$
To fly back to the original destination, the pilot needs to fly 48.5 miles east and 24.1 miles north. We can find the distance $d$:
$d = \sqrt{(48.5~mi)^2+(24.1~mi)^2} = 54.2~mi$
We can find the direction north of east:
$tan~\theta = \frac{24.1~mi}{48.5~mi}$
$\theta = tan^{-1}(\frac{24.1~mi}{48.5~mi})$
$\theta = 26.4^{\circ}$
(b) We can find the extra distance the pilot must fly:
$55~mi+25~mi+54.2~mi = 134.2~mi$