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Finding a Side Length, Quadrilaterals

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November 10, 2005
trigonometryquadraticsalgebraquadratic formulatrig identitiesLaw of Cosines

Problem Statement

In quadrilateral ABCDABCD, BC=8BC=8, CD=12CD=12, AD=10AD=10, and m∠A=m∠B=60∘m\angle A= m\angle B = 60^\circ. Given that AB=p+qAB=p + \sqrt{q}, where pp and qq are positive integers, find p+qp+q.
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