Answer
$MB=\sqrt 73$
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 $AB$.
$AC^{2}+CB^{2}=AB^{2}$
$a^{2}+ 8^{2}=10^{2}$
Simplify...
$a^{2}+64=100$
Subtract 64 from both sides...
$a^{2}=36$
Square root both sides...
$a=6$ OR $AC=6$
Since $M$ is the midpoint of $AC$, $AM=3$ and $MC=3$
Using the Pythagorean Theorem (again) we can find the length of $MB$.
$MC^{2}+CB^{2}=MB^{2}$
$3^{2}+ 8^{2}=c^{2}$
Simplify...
$9+64=c^{2}$
Combine like terms...
$73=c^{2}$
Square root both sides...
$c=\sqrt 73$ OR $MB=\sqrt 73$
