Two airplanes take off from one airfield at noon. One flies due east a

This is the diagram I get from the information given. One plane due east 400 miles and other plane north-east 566 miles. Approximate answer is required.


My problem is that the only time when I know what to do with a 45 degree angle is when it is in a right triangle. But I do not know if this is a right triangle. But the good thing I know about GMAT is that they ask me questions based on some basic concepts only. They may twist the concepts so that it is hard to recognize but they will still test me on the same concepts. So I use this weakness of GMAT to find out whether this is a right triangle.
If it is a right triangle, its other two angles will be 45 each and hence AB will be 400. This means the hypotenuse will be \(400\sqrt{2}\). Since \(\sqrt{2}\) is close to 1.4, 400*1.4 = 560, close enough to 566. Hence the approximate value of AB is indeed 400 and this is a right angled triangle.
Of course, if this triangle weren't right angled, we could still get AB. Substitute 800 in place of 566 and try, if it interests you.