Answer:
The hikers are 5.9 miles apart.
Step-by-step explanation:
Let O represents the base camp,
Suppose after walking 3.5 miles west, first hiker's position is A, then after going 1.5 miles north from A his final position is B,
Similarly, after walking 2 miles east, second hiker's position is C then going towards 0.5 miles south his final position is D.
By making the diagram of this situation,
Let D' is the point in the line AB,
Such that, AD' = CD
In triangle BD'D,
BD' = AB + AD' = 1.5 + 0.5 = 2 miles,
DD' = AC = AO + OC = 3.5 + 2 = 5.5 miles,
By Pythagoras theorem,
![BD^2 = BD'^2 + DD'^2](https://tex.z-dn.net/?f=BD%5E2%20%3D%20BD%27%5E2%20%2B%20DD%27%5E2)
![BD = \sqrt{2^2 + 5.5^2}=\sqrt{4+30.25}=\sqrt{34.25}\approx 5.9](https://tex.z-dn.net/?f=BD%20%3D%20%5Csqrt%7B2%5E2%20%2B%205.5%5E2%7D%3D%5Csqrt%7B4%2B30.25%7D%3D%5Csqrt%7B34.25%7D%5Capprox%205.9)
Hence, the hikers are 5.9 miles apart.