To solve using parallelogram method, draw the two vectors on the same initial point. (See Fig.1 in the attachment.)
Then, draw another two lines in such a way that a parallelogram is formed. (See Fig.2)
The angle between the two vectors is:
Applying the property of a parallelogram --- consecutive angles are supplementary, then the other angle is:
`180^o - 110^o=70^o`
And draw a diagonal starting from the initial position. This represents the resultant vector. (See Fig.3)
To solve for the magnitude of the resultant vector, apply Cosine Law.
To solve for theta, apply Cosine Law again.
`theta = cos^(-1)((45^2+65.19^2-65^2)/(-2*45*65.19))`
Using the East axis as the reference for its direction, then the direction of the resultant vector is:
`theta_f = 69.55^o - 35^o`
`theta_f =34.55^o` (See Fig.4)
Therefore, the final position of the plane is 65.19km away from its starting point, and its direction is 34.55 degree North of East.