This is an interesting geometry problem from an SAT practice exam.

In triangle $UVW$, the measure of $\angle U$ is $90$ degrees, $WV=39$, and $UV=36$. Triangle $XYZ$ is similar to triangle $UVW$, where $\angle X$, $\angle Y$, and $\angle Z$ correspond to $\angle U$, $\angle V$, and $\angle W$, respectively. If each side of triangle $XYZ$ is $3/5$ the length of its corresponding side of triangle $UVW$, what is the value of $cos\ Z$?

Check out the solution and discussion here.

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