Answer to Question #1934 in Trigonometry for Neil

Question

A ship travels 18.5 km on a course of 31.2 degrees south of east, then 12.7 km due south, then 21.5 km on the course of 61.3 degrees west of south, where it lands. Find the displacement and the angle traveled from the starting point to the landing point.

Answer 1

Let’s find projections of the vector of displacement.
V_x = 18.5*cos31.2 - 21.5*sin61.3 ≈ -3.0344
V_y = 18.5*sin31.2 + 12.7 + 21.5*cos61.3 ≈ 32.6083
Displacement = √(V_x²+V_y² ) = 32.7492
Angle = 90 - arctan((|V_y|)/(|V_x|)) ≈ 5.333 degrees to the west of south.