Halliday, Resnick & Walker — Motion in Two and Three Dimensions: Problem 86

A radar station detects an airplane approaching directly from the east. At first observation, the airplane is at distance \(d_1 = 360 \text{ m}\) from the station and at angle \(\theta_1 = 40^\circ\) above the horizon (Fig. 4.29). The airplane is tracked through an angular change \(\Delta\theta = 123^\circ\) in the vertical east–west plane; its distance is then \(d_2 = 790 \text{ m}\). Find the (a) magnitude and (b) direction of the airplane’s displacement during this period.