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 kilometers

Answer 2

\[\sqrt{10^2-6^2}=8\]

Answer 3

The shape that is created by this info is a right triangle, where the hypotenuse is 10, and the leg is 8. Using the pythagorean formula, with c = 10, and a (or b) = 6, we get:
\[c^{2} = a^{2} +b^{2} \Rightarrow 10^{2} = 6^{2} +b^{2}\]
Solving for b gives you 8