Re: Two Olympiad Problems
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You don't have to use trigonometry to prove that the height is maximized when the triangle is isoceles. You can use the triangle inequality after adding a reflected copy of the triangle above. So, this whole problem can be done without calculus.
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All calculus problems can be done without calculus. When my father was teaching mathematical logic at City College he would sometimes ask for a calculus problem and demonstrate.
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