A plane is 150 miles north and 100 miles east of an airport. What bearings should be taken to fly directly to the airport?

You need a drawing to understand more properly. Having done so will show you that you have a right angled triangle. Use the tangent rule to find the angle you need. However, remember that bearings are according to the north.

Tmporarily do the follwing. Put the airport at the origin. Draw where the plane is. Now move the triangle that you drew so the plane is at the origin.

Now you should be able to calculate bearing.

But it's for you to do the drawing! Ok, here it goes:

By using tangent rule, you have angle inside the triangle, at the plane. To have the bearing, do 360 degrees minus 90 degrees and minus the angle you obtained from the tangent rule.

tan \theta = \frac{150}{100}