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a, 2a, 180-3a Triangle

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April 23, 2009
trigonometryquadratics

Problem Statement

If \left|BC\right| \equal{} a, \left|AC\right| \equal{} b, \left|AB\right| \equal{} c, 3\angle A \plus{} \angle B \equal{} 180{}^\circ and 3a \equal{} 2c, then find b b in terms of a a.
<spanclass=′latex−bold′>(A)</span> 3a2<spanclass=′latex−bold′>(B)</span> 5a4<spanclass=′latex−bold′>(C)</span> a2<spanclass=′latex−bold′>(D)</span> a3<spanclass=′latex−bold′>(E)</span> 2a33<span class='latex-bold'>(A)</span>\ \frac {3a}{2} \qquad<span class='latex-bold'>(B)</span>\ \frac {5a}{4} \qquad<span class='latex-bold'>(C)</span>\ a\sqrt {2} \qquad<span class='latex-bold'>(D)</span>\ a\sqrt {3} \qquad<span class='latex-bold'>(E)</span>\ \frac {2a\sqrt {3} }{3}
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