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Find x in triangle ABC

Source: AHSME 1963 Problem 34

January 11, 2014
trigonometrytrig identitiesLaw of CosinesAMC

Problem Statement

In triangle ABC, side a=3a = \sqrt{3}, side b=3b = \sqrt{3}, and side c>3c > 3. Let xx be the largest number such that the magnitude, in degrees, of the angle opposite side cc exceeds xx. Then xx equals:
<spanclass=′latex−bold′>(A)</span> 150<spanclass=′latex−bold′>(B)</span> 120<spanclass=′latex−bold′>(C)</span> 105<spanclass=′latex−bold′>(D)</span> 90<spanclass=′latex−bold′>(E)</span> 60<span class='latex-bold'>(A)</span>\ 150 \qquad <span class='latex-bold'>(B)</span>\ 120\qquad <span class='latex-bold'>(C)</span>\ 105 \qquad <span class='latex-bold'>(D)</span>\ 90 \qquad <span class='latex-bold'>(E)</span>\ 60
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