VMO 1963 Problem 5

The triangle $ABC$ has semiperimeter $p$ . Find the side length $BC$ and the area $S$ in terms of $\angle A$ , $\angle B$ and $p$ . In particular, find $S$ if $p \approx 23.6$ , $\angle A \approx 52^{\circ}42'$ , $\angle B \approx 46^{\circ}16'$ .