Answer
$MN=4$
Work Step by Step
Using the Pythagorean Theorem we can find the length of $AC$.
$a^{2}+b^{2}=c^{2}$
Remember, the hypotenuse is always the longest side, or the side opposite the right angle, in this case $AB$.
$AC^{2}+CB^{2}=AB^{2}$
$a^{2}+ 15^{2}=17^{2}$
Simplify...
$a^{2}+225=289$
Subtract 225 from both sides...
$a^{2}=64$
Square root both sides...
$a=8$ OR $AC=8$
$MN$ is the mid-segment of $\triangle ABC$. A triangle's mid-segment is half the length of the parallel side. If $AC=8$, then $MN$ equals half that length or, $MN=4$.
