The sides of a parallelogram are 3cm and 5cm and include an angle 144. Find the lengths of the diagonals of the parallelogram.
Let the diagonal lengths be $a$ and $b$. Note that the diagonal of a parallelogram splits the shape into two congruent triangles. Using the Law of Cosines on one of the triangles, we get \begin{align*}
a^2&=3^2+5^2-2(3)(5)\cos 144\\
&=34+30\cos 144\\
&=34+30\cos(-36)\\
&=34+30\cos 36.
\end{align*}By symmetry, both diagonals are of equal length, so $a=b=\boxed{\sqrt{34 + 30\cos 36}}$ centimeters.