AHSME 1995 Problem 23

The sides of a triangle have lengths $11,15,$ and $k$, where $k$ is an integer. For how many values of $k$ is the triangle obtuse? $\mathrm{(A) \ 5 } \mathrm{(B) \ 7 } \mathrm{(C) \ 12 } \mathrm{(D) \ 13 } \mathrm{(E) \ 14 }$