Question 19In $\triangle ABC,$ $M$ is the midpoint of side $BC,$ $AN$ bisects $\angle BAC,$ $BN\perp AN,$ and $\theta$ is the measure of $\angle BAC.$ If sides $AB$ and $AC$ have lengths $14$ and $19,$ respectively, then length $MN$ equals $2$$\frac52$$\frac52-\sin\theta$$\frac52-\frac12\sin\theta$$\frac52-\frac12\sin\left(\frac\theta2\right)$