Question

A man has a map for a treasure. The following three displacements lead to the point in the field where the treasure is buried, if he starts from his home. A: 72.4 m, 32.0° east of north B: 57.3 m, 36.0° south of west C: 17.8 m due south - How far is the treasure from the man's home and in what direction?

Answer 1

$$s_x=72.4\sin{32}-57.3\cos{36}+17.8(0)\\=-7.99\ m\\ s_y=72.4\cos{32}-57.3\sin{36}-17.8\\=9.92\ m\\s=\sqrt{7.99^2+9.92^2}=12.7\ m$$

$$\theta=\arctan{\frac{7.99}{9.92}}=38.9\degree{ W of N}$$