Question

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. How far did the runners travel north?
4 km
8 km
10 km

Answer 1

This forms a right triangle with 6 being the base and 10 being the hypotenuse.

Using the Pythagorean theorem solve the distance north, which would be the height of the right triangle.

X = √(10^2 - 6^2)

X = √(100-36)

X = √64

X = 8

The answer is 8 km.

Answer 2

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 :

$Hypotenuse^2=Perpendicular^2+Base^2$

$AC^2=CB^2+AB^2$

$10^2=CB^2+6^2$

$10^2-6^2=CB^2$

$\sqrt{10^2-6^2}=CB$

$8=CB$

Hence the runners travel north is 8 km