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Triangle Log Problem

Source: Irish MO 1988

May 2, 2012
trigonometrylogarithmsgeometry unsolvedgeometry

Problem Statement

Problem: A mathematical moron is given the values b; c; A for a triangle ABC and is required to fi nd a. He does this by using the cosine rule a2=b2+c2−2bccosA a^2 = b^2 + c^2 - 2bccosA and misapplying the low of the logarithm to this to get loga2=logb2+logc2−log(2bccosA) log a^2 = log b^2 + log c^2 - log(2bc cos A) He proceeds to evaluate the right-hand side correctly, takes the anti-logarithms and gets the correct answer. What can be said about the triangle ABC?
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