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?

Answer 1

Answer:

Step-by-step explanation:

alright lets get started.

Please refer the diagram I have attached.

the runner traveled, six kilometers east.

Next, they turn to north and suppose they run x kilometers.

The starting and the ending points distance is 10 kilometers.

There will be a right triangle formed, we can find the value of x by using Pythagorean theorem.

$a^2+b^2=c^2$

$6^2+x^2=10^2$

$36+x^2=100$

Subtracting 36 from both sides

$x^2=100-36=64$

$x=8$

So, the runners travel 8 kilometers to the north.     :    answer

Hope it will help.  :)

Answer 2

Answer:

8 km

Step-by-step explanation:

Data

• First the runners go 6 km east

• Next they go x kilometers north until they finish the race  (where x is an unknown amount)

• The finish line is 10 kilometers from the starting line  

Then, a rectangular triangle is formed, 10 km is the hypotenuse, 6 km is one side and x km is the other side. From Pythagoras theorem:

10^2 = 6^2 + x^2

100 - 36 = x^2

x = sqrt(64)

x = 8 km