Chintito
The second one has, effectively, been answered between Alex and Aim High, i.e. Aim high provided 2 answers, Alex said why it is the second.
The first question is not like any I expect you to find in the exam, although it is interesting. The key is to understand that the whole reason we ever bother with Earth Convergence is that it tells us how the bearing of a great circle changes, depending on where it is measured. Therefore the change in great-circle bearing is equal to Earth Convergence.
So the change in GC bearing from 008°E (bearing 084°T) to F (at 024°E, bearing 092°, reciprocal of 272°) is 8°. Therefore the convergence is 8°, and ch. long. x sin mean lat = 8°. Since ch. long. is 16°, mean lat must be inverse sin 1/2, which is 30°. From this point approximation is the only option, unless you want maths way beyond ATPL level. Assume the same change of latitude between 'E' and 008°E as between 008°E and 'F', you're at 30°N 3/4 of the way up the track from 27°N, so, F is at 31°N.
The rest is simple. Earth Convergence between E and F is ch. long. sin mean lat = 32 x sin 29° = 15.5°. The question shows that tracks are decreasing westward (a diagram confirms this) so since F from E measured at F is 092° the same line measured at E is 092° - 15.5° = 76.5°.
That is a scratch calculation for an unusual question after 3 pints, so I will not be offended if anyone has anything to add.
Note to all students: this is beyond ATPL General Navigation requirements. I just enjoy a challenge. Sad, I know
