Contestants in a long distance race run 5 kilometers due south. the runners then turn right and head west towards the finish line. if the straight line distance from start to finish is 13 kilometers, what is the distance that the contestants traveled while heading west? 12 km 14 km 17 km

The distance they ran makes a triangle, if you draw it out and solve for the missing side, the missing line is 12km, hope that helps

So if 13 km is the longest side, then the empty side has to be in the middle of the 2, which the only answer that fits it is 12. 

Or you can do it the original way. 

for the equation, you would have to bring c squared, which is 13, over to the side with 5 so the blank side is by itself. 

so then square 13 and 5 

13 squared is 169 

5 squared is 25 

subtract 

169-25=144 

144's square root is 12 

so there is your answer is 12 km.