+585 In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 8$, $SU = 8$, $TU = 8$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$, then what is $SX$?
0 We have X is the centroid as altitude and median are the same thing in an equilateral triangle, therefore:
\(\frac{SX}{XN}=2\)
Also using pythagorean theroem on \(\triangle STN\) we get:
\(SN=4\sqrt3\)
Therefore:
\(\boxed{SN=\frac{8\sqrt{3}}{3}}\)
