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A mathematical moron is given two sides and the included angle of a triangle and attempts to use the Law of Cosines:

a^2 = b^2 + c^2 - 2bc \cos A,

to find the third side

a.

He uses logarithms as follows. He finds

\log b

and doubles it; adds to that the double of

\log c;

subtracts the sum of the logarithms of

2, b, c,

and

\cos A;

divides the result by

2;

and takes the anti-logarithm. Although his method may be open to suspicion his computation is accurate. What are the necessary and sufficient conditions on the triangle that this method should yield the correct result?

B1

Problems(1)