A hiker makes four straight-line walks A 32 km at 140 ◦ B 27 km at 291 ◦ C 12 km at 55 ◦ D 18 km at 302 ◦

Question

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.

Answer 1

Hi Elizabeth G.,

Use vectors:

A = 30cos(140) i +30sin(140) j

B = 27cos(291) i + 27sin(291) j

C = 12cos(55) i + 12sin(55) j

D = 18cos(302) i + 18sin(302) j

A + B + C + D = 3.12 i - 11.36 j = V, this is the vector from the origin.

| V | = √[(3.12)^2 + (-11.36)^2] = 11.78 km, the magnitude of vector V is the distance from the origin.

I hope this helps, Joe.