Moderate# Applications, Cell Towers, Inverse Function Law of Cosines

TRIG-NN7X4P

Two cell phone towers, towers ‘A’ and ‘B’, lie on an East-West line and are $45\ miles$ apart from each other. A targeted cell phone is $38\ miles$ from tower ‘A’ and $23\ miles$ from tower ‘B’ in a generally northern direction. A 'bearing' measurement is a method of measuring the number of degrees an object is from true north and moving in a clockwise direction. As an example, if an object is due East then it is on a bearing of ${90}^{°}$.

What is the ‘bearing’ of the signal from tower ‘A’ to the cell phone? Round your answer to the nearest tenth of a degree.