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AC^2+AB^2=BC^2


15^2+AB^2=17^2


AB^2=17^2-15^2


AB^2=8^2


AB=8
Use Pythagorean Theorem. 

15^2+b^2=17^2.

First is exponents.
225+b^2=289

Next get b^2 by itself.
b^2=64

The square root of 64 is 8.