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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?

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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.

[tex]a^2+b^2=c^2[/tex]

[tex]6^2+x^2=10^2[/tex]

[tex]36+x^2=100[/tex]

Subtracting 36 from both sides

[tex]x^2=100-36=64[/tex]

[tex]x=8[/tex]

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

Hope it will help.  :)

Ver imagen stokholm

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

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