Answer:
280°
Explanation:
We can use the law of cosines to find the distance back to the airport. The internal angle at the first turning point is ...
180° -(128° -30°) = 82°
The law of cosines tells us ...
a^2 = b^2 +c^2 -2bc·cos(A)
a^2 = 200^2 +400^2 -2·200·400·cos(82°) ≈ 177,732.3
so the distance home is ...
a ≈ √177,732.3 ≈ 421.58 . . . . miles
Now, the law of sines can be used to find the internal angle at C.
sin(C)/c = sin(A)/a
C = arcsin(c/a·sin(A)) = arcsin(400/421.58·sin(82°)) ≈ arcsin(0.939571)
C ≈ 69.98°
This angle, added to the original bearing of 30° is 99.98°, which is the opposite of the bearing home. That must be 180° +99.98° = 279.98°.
The true bearing for return to the airport is 280°.