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 \(10\sqrt{3}\).