Answer
$a=8,b=6$
Work Step by Step
As per the given figure, we have
$a^2+b^2=10^2$ and $a^2+(b+9)^2=17^2$
Let us subtract the above equations.
We get $b^2-(b+9)^2=100-289$ or, $-18b=-108$
or, $b=6$
Now, plug the value of $b=6$ in the equation: $a^2+b^2=10^2$, we get $a^2=100-36$
or, $a=8$
Hence, $a=8,b=6$