Bearing of Airplane?

Question

A plane leave a certain airport from runway 4 RIGHT, whose bearing is N40degreesE. After flying for 1/2 mile, the pilot requestd permission to trun 90 degrees and head toward the southeast. The permission is granted. After the airplane goes 1 mile in this direction, what bearing should the control tower use to locate the plane?

After my work, I got S23.4degreesE but the book's answer is
S76.6degreesE.

How do I get the book's answer? Why is my answer wrong?

Answer 1

On his 1st leg he goes to (in +x=east,+y=north coordinates) (+3.213938D-001, +3.830222D-001) mi
On the 2nd leg, (+7.660444D-001, -6.427876D-001) mi
sum is (+1.087438247960D+000, -2.597653881279D-001) mi
angle = arctan(y/x) = -13.435 deg in x-y coords, 103.435 deg in clockwise-from-North coordinates. That equates to the book's answer 76.565 deg E of S.

Answer 2

This is a curious answer. Assuming no wind to deflect the course of the airplane in flight a magnetic heading and a ninety degree turn the Pilot would be heading would be 130 degrees (40 plus 90) and your compass heading would read 130 degrees heading. This is a southeasterly heading. And this course could be held without input to offset the effects of wind in a zero wind or true headwind condition of flight. Or, held when adjusted for the force of wind in flight on the aircraft.

Of course the tower could identify the aircraft flying a bearing of 130 degrees however the relative bearing to the tower is another matter altogether.