A triangle has area $20$, one side of length $8$, and the median to that side of length $6$. Let $\theta$ be the acute angle formed by that side and the median. What is $\sin\theta$?

1. The median splits the triangle into two triangles each with base (side$/2$) and the median, sharing supplementary angles $\theta,180^\circ-\theta$ (same sine): total area $=\left(\frac{\text{side}}2\right)\cdot\text{median}\cdot\sin\theta$.
2. $\sin\theta=\dfrac{2\cdot\text{area}}{\text{side}\cdot\text{median}}=\dfrac{2(20)}{8\cdot6}=\dfrac{40}{48}=\boxed{\dfrac56}$.