How far from the starting point is the hiker after these four legs of the hike? All angles are measured in a counter-clockwise direction from the positive x-axis. Answer in units of km

Question

A hiker makes four straight-line walks A 12 km at 86 ◦ B 23 km at 222 ◦ C 17 km at 172 ◦ D 31 km at 122 ◦ in random directions and lengths starting at position (41 km, 41 km),

Answer 1

Convert each leg into x and y component ... sum all four legs to find total x and total y ... sqrt of sum of squares to find resultant distance = 55.6