Answer to Question #138637 in Physics for rods

Question

A student walks to school 10m due East, 5m at 30 degrees North of East, 6m at 45 degrees North of West, and 8m West. How far has he traveled?

Answer 1

$$s_1=(10,0)\ m\\s_2=(5\cos{30},5\sin{30})\ m\\s_3=(-6\cos{45},6\sin{45})\ m\\s_4=(-8,0)\ m\\s_y=5\sin{30}+6\sin{45}=6.74\ m\\s_x=10-8+5\cos{30}-6\cos{45}=2.09\ m\\s=\sqrt{2.09^2+6.74^2}=7.1\ m$$

$$\theta=\arctan{\frac{2.09}{6.74}}=17\degree\text{E of N}$$