AMC 10 2008b Problem 15

How many right triangles have integer leg lengths $a$ and $b$ and a hypotenuse of length $b+1$, where $b<100$? $\mathrm{(A)}\ 6 \mathrm{(B)}\ 7 \mathrm{(C)}\ 8 \mathrm{(D)}\ 9 \mathrm{(E)}\ 10$