find B

$C=\sqrt{{A}^{2}-{B}^{2}}$

where we know that; $C=8$ and; $A=17$

just put those numbers in for now;

$8=\sqrt{{17}^{2}-{B}^{2}}$

we need ${A}^{2}$--${B}^{2}$to equal ${8}^{2}$ therefore;

${17}^{2}-{B}^{2}=64$

Minus 64 from both sides;

${17}^{2}-{B}^{2}-64=0$

Then add ${B}^{2}$ to both sides;

${17}^{2}-64={B}^{2}$

${17}^{2}-64$ is equal to $225$

therefore ${B}^{2}=225$

and $B=15$