Aship sets out to sail to a point 103 km due north. an unexpected storm blows the ship to a point 125 km due east of its starting point. (a) how far and (b) in what direction (as an angle from due east, where north of east is a positive angle) must it now sail to reach its original destination?

So! I have written out most of the working but ran out of space so will explain a bit here. Basically, by drawing out a diagram we can see that you have a right angled triangle, and you also know the lengths of two sides of said triangle. With this information, in order to find the distance travelled, you just need to use Pythagoras' theorem (as shown - x in the diagram is the distance the boat travels to correct itself).
For the angle, notice how it wants it relative to due east - as we have a triangle we can use to work out internal angles with trig, here I would find it easiest to find the boat's initial angle in terms of due west, then take that away from 180 to find the larger angle! I don't have a calculator with trig buttons on with me, but if you type the tan sum into a scientific calculator to find the west angle, then subtract that from 180 you'll have your answer.