1981 AHSME Problems/Problem 21
In a triangle with sides of lengths , , and , . The measure of the angle opposite the side length is
We will try to solve for a possible value of the variables. First notice that exchanging for in the original equation must also work. Therefore, works. Replacing for and expanding/simplifying in the original equation yields , or . Since and are positive, . Therefore, we have an equilateral triangle and the angle opposite is just .
This looks a lot like Law of Cosines, which is . is , so the angle opposite side is .