Partial Derivatives & the Gradient · Medium problem

A triangular plot has two sides of length $a=10$ m and $b=10$ m with the included angle $C=\dfrac{\pi}{3}$ fixed exactly. Both $a$ and $b$ were each measured with a possible error of $0.1$ m. Using differentials on $A = \dfrac12 ab\sin C$, find the maximum possible error in the computed area (in m$^2$). Give an exact answer in simplest radical form.