Answer:
8 km
Step-by-step explanation:
Given : Runners in a long distance race start out going 6 kilometers east and then head north for the remainder of the race.
The finish line is 10 kilometers from the starting line.
To Find: How far did the runners travel north?
Solution :
Refer the attached figure
Runners in a long distance race start out going 6 kilometers east i.e. AB = 6 km
The finish line is 10 kilometers from the starting line.i.e. AC = 10 km
We are supposed to find How far did the runners travel north i.e.CB
So, we will use Pythagoras theorem :
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
[tex]AC^2=CB^2+AB^2[/tex]
[tex]10^2=CB^2+6^2[/tex]
[tex]10^2-6^2=CB^2[/tex]
[tex]\sqrt{10^2-6^2}=CB[/tex]
[tex]8=CB[/tex]
Hence the runners travel north is 8 km
