In $\triangle{DEF}$, shown in the figure below, $\overline{EG}$ is an altitude, $\angle{DEF}$ is a right angle, $EF=20$ centimeters, and the measure of $\angle{EDF}$ is $30^\circ$. What is $EG$, in centimeters?

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When an altitude is drawn in a right triangle, the 2 triangles formed and the orginal triangle will be similar.

All triangles are $30-60-90$ special triangles.

The ratios of a $30-60-90$ triangle are $1:\sqrt{3}:2$. For triangle $\triangle{EGF}$, the hypotenuse is $20$, the short side is $10$, and the longer side is $10\sqrt{3}$.