Question

What is the resultant of a displacement 6.0 miles North and one 9.0 miles East?

Answer 1

$$d=\sqrt{d_x^2+d_y^2}=\sqrt{9.0^2+6.0^2}=11\:\rm mi$$

$$\theta=\tan^{-1}\frac{d_y}{d_x}\\=\tan^{-1}\frac{6.0}{9.0}=34^\circ\quad \rm N\; of\; E$$