The length of BC is 15 units.
I used the Pythagorean theorem to find this. 8 is the length of the given leg, and 17 is the length of the hypotenuse:
8²+b²=17²
64+b²=289
Subtract 64 from both sides:
64+b²-64=289-64
b²=225
Take the square root of both sides:
√b²=√225
b=15