A mathematical moron is given the values b, c, A for a triangle ABC and is required to find the value of a. He does this by using the cosine rule

a

^{2}= b

^{2}+ c

^{2}- 2bc.cosA

and misapplying the law of logarithms to this to get

log(a

^{2}) = log(b

^{2}) + log(c

^{2}) - log(2bc.cosA).

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?

[ Irish MO 1988 Paper 1 Question 4]

The wording is genuine :-)

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