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

8 km

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

Answer 2

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. :)