Question

An explorer hikes 4 miles due east, 7 miles due south, then 3 miles due east, then 1 mile due north, and finally then 2 miles due west. How far is he from his original position?

Answer 1

Answer:

7.81 miles

Step-by-step explanation:

Assume Eastern and Southern displacement as positive and Northern and Western displacement as negative, the explorer's East-West and South-North displacements were:

$E=4+3-2=5\ miles\\S=7-1=6\ miles$

His distance from his original position is:

$D^2 = E^2+S^2\\D=\sqrt{5^2+6^2}\\ D= 7.81\ miles$