CEMC Euclid, 2008

Geometry Difficulty 3.0 AMC 10/12 Prove it Canada

In the diagram, $AB = 21$ and $BC = 16$ . Also, $\angle ABC = 60^\circ$ , $\angle CAD = 30^\circ$ , and $\angle ACD = 45^\circ$ . Determine the length of $CD$ , to the nearest tenth.

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