Find Airplane Bearing

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?

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  1. let's give some letter names to our triangle
    let the origin be O
    let the end of the first leg be A, the end of the second leg be B

    then OA=.5 and AB = 1 and angle A = 90º
    so by Pythagoras OB = 1.118

    and angle AOB = 63.4
    so the plane is flying 103.43 from north
    which when subtracted from 180 is 76.57º as your book says

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