Question

From base camp, a hiker walks 3.5 miles west and 1.5 miles north. Another hiker walks 2 miles east and 0.5 miles south. To the nearest tenth of a mile how far apart are the hikers

Answer 1

The hikers are 5.9 miles apart.

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`

`BD = √(2^2 + 5.5^2)=√(4+30.25)=√(34.25)\approx 5.9`

Hence, the hikers are 5.9 miles apart.