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

8 km

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`

`√(10^2-6^2)=CB`

`8=CB`

Hence the runners travel north is 8 km

Answer 2

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.