



 
Hi Kristin, The important measurement is the length of the fighter's arm. In my diagram $S$ is his shoulder and $F$ is the fist at the end of his arm. I drew a horizontal line from $F$ and a vertical line from $S$ to meet at a point $P.$ The distance from $S$ to $F$ is the length of the fighter's arm which I will cal $a.$ The distance from $F$ to $P,$ which I will call $d$ is the distance between the two men. The measure of angle $PSF$ is $45^o$ and hence the measure of the angle $SFP$ is also $45^o.$ The triangle $SFP$ is thus an isosceles triangle and the length of the side $PS$ is therefore $d.$ Triangle $SFP$ is a right triangle and hence Pythagoras Theorem tells us that \[d^2 + d^2 = a^2 \mbox{ or } d^2 = \frac{a^2}{2}\] Thus the distance between the two men is \[d = \frac{a}{\sqrt{2}}\] I hope this helps,  


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