The following problem appeared on the American High School Mathematics Examination (now called the AMC 12) in 1988:

If , what is ?

When I presented this problem to a group of students, I was pleasantly surprised by the amount of creativity shown when solving this problem.

Yesterday, I presented a solution using triangles. Here’s a second solution that I received: begin by squaring both sides and using a Pythagorean trig identity.

We use the Pythagorean identity again to find :

Therefore, we know that

,

so the answer is either or . However, this was a multiple-choice contest problem and was not listed as a possible answer, and so the answer must be .

For a contest problem, the above logic makes perfect sense. However, the last step definitely plays to the fact that this was a multiple-choice problem, and the concluding step would not have been possible had been given as an option.

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*Posted by John Quintanilla on September 21, 2015*

https://meangreenmath.com/2015/09/21/different-ways-of-solving-a-contest-problem-part-2/

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