CEMC Euclid, 2004

Geometry Difficulty 3.0 AMC 10/12 Prove it Canada

In the diagram, a drawer, $PRST$ , that is $11$ cm high is in a long slot, $ABCD$ , which is $15$ cm high. The drawer is pulled out so that the midpoint of its base rests at $C$ . The drawer is tilted so that the top back edge of the drawer touches the top of the slot. If the angle between the drawer and the slot is $10°$ , determine the length of the drawer, to the nearest tenth of a centimetre.

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